Is there such a thing as a future infinitive in English?

In tenses where we can't use auxiliary verbs, will is replaced by going to:

John is said to be going to leave for good.

However, most of the time we'd just use the present continuous, even though it's a future event:

John is said to be leaving for good.

Future Infinitives?

I don’t mean to detract from the clarity and correctness of Peter Shor’s answer. You should use what he said to use here. I’d like to address the theoretical notion of “future infinitives” in English.

Mind you, Ancient Latin did have infinitives inflected for tense and voice, and Modern Portuguese today has so-called “personal” infinitives which are inflected for person and number.

But not English. You cannot inflect an English infinitive.

What English does have

Here are the four most common infinitive constructions in English:

1. infinitive: to hold him responsible
2. perfect infinitive: to have held him responsible
3. passive infinitive: (for) him to be held responsible
4. perfect passive infinitive: (for) him to have been held responsible

There is no future to be seen there. That’s because the infinitive in English — such as be, have, go, or hold — is morphologically inert: it lacks any vestige of inflectional morphology. Try as you may, you cannot fiddle its internal bits to produce some alternate form of the base verb that now expresses traits like its person or number, time or mood, voice or aspect, or even its grammatical relationships with other syntactic constituents.

It’s not that English is incapable of expressing those traits in its infinitive constructions. You simply have to include various extra words along with your infinitives when you want to express those ideas.

So let’s look at some of those specific approaches in the context of your question.

Concrete Approaches

Here we talk about a past event in various ways:

• John left yesterday. (a past event)
• They say that John left yesterday. (a past event described in the present)
• They said that John left yesterday. (a past event described in the past)
• They will say that John left yesterday. (a past event described in the future)
• It is said that John left yesterday. (a past event described in the present)
• It was said that John left yesterday. (a past event described in the past)
• It will be said that John left yesterday. (a past event described in the future)
• John is said to have left yesterday. (a past event described in the present)
• John was said to have left yesterday. (a past event described in the past)
• John will be said to have left yesterday. (a past event described in the future)

Just keep in mind that this version also talks about a past event in the present, but it has the added connotation that you're sure he did so:

• John will have left yesterday. (a past event you're sure of)

Which leads to this sort of thing:

• They say that John will have left yesterday. (a past event you're sure of described in the present)
• They said that John will have left yesterday.(a past event you're sure of described in the past)
• They will say that John will have left yesterday. (a past event you're sure of described in the future)
• John is said to have left yesterday. (a past event you're sure of described in the present)
• John was said to have left yesterday. (a past event you're sure of described in the present)
• John will be said to have left yesterday. (a past event you're sure of described in the future)

Here we talk about a future event in various ways:

• John will leave tomorrow. (a future event)
• They say that John will leave tomorrow. (a future event described in the present)
• They said that John would leave tomorrow. (a future event described in the past)
• They will say that John will leave tomorrow. (a future event described in the future)
• It is said that John will leave tomorrow. (a future event described in the present)
• It was said that John would leave tomorrow. (a future event described in the past)
• It will be said that John will leave tomorrow. (a future event described in the future)

However, these versions don't sound as good:

• John is said to leave tomorrow. (a future event described in the present)
• John was said to leave tomorrow. (a future event described in the past)
• John will be said to leave tomorrow. (a future event described in the future)

That's because we prefer to use be plus a nonfinite verb form to talk about the "normal" present in English. Here are three ways, of which the last is the most customary:

• John leaves today. (present of leave)
• John is to leave today. (present of be to plus infinitive of leave)
• John is leaving today. (present of be plus progressive of leave)

Choosing the last of those, meaning be plus a progressive, makes it easier to convert to your formulation using John is said to plus the infinitive:

• John is said to be leaving today. (present of be said to plus infinitive of be leaving)
• John was said to be leaving today. (past of be said to plus infinitive of be leaving)
• John will be said to be leaving today. (present of be said to plus infinitive of be leaving)

Those can all also refer to future events—and arguably, they already do so. You can make this shift in time more obvious by changing today to tomorrow.

• John leaves tomorrow. (a future event described in the present)
• John is to leave tomorrow. (a future event described in the present)
• John is leaving tomorrow. (a future event described in the present)

Which leads to your be said to forms in this way:

• John is said to leave tomorrow. (a future event described in the present)
• John was said to leave tomorrow. (a future event described in the past)
• John will be said to leave tomorrow. (a future event described in the future)
  
  
• John is said to be leaving tomorrow. (a future event described in the present)
• John was said to be leaving tomorrow. (a future event described in the past)
• John will be said to be leaving tomorrow. (a future event described in the future)
• John will have been said to be leaving tomorrow. (a future event described in the past with certainty)

And a very great many they say variants:

• They say that John is leaving tomorrow. (a future event described in the present)
• They say that John will be leaving tomorrow. (a future event described in the present)
• They say that John is to leave tomorrow. (a future event described in the present)
• They say that John is to be leaving tomorrow. (a future event described in the present)
  
  
• They said that John is leaving tomorrow. (a future event described in the past)
• They said that John was leaving tomorrow. (a future event described in the past)
• They said that John would be leaving tomorrow. (a future event described in the past)
• They said that John was to leave tomorrow. (a future event described in the past)
• They said that John was to be leaving tomorrow. (a future event described in the past)
  
  
• They will have said that John is leaving tomorrow. (a future event described in the past with certainty)
• They will have said that John was leaving tomorrow. (a future event described in the past with certainty)
• They will have said that John would be leaving tomorrow. (a future event described in the past with certainty)
• They will have said that John was to leave tomorrow. (a future event described in the past with certainty)
• They will have said that John was to be leaving tomorrow. (a future event described in the past with certainty)
  
  
• They will say that John leaves tomorrow. (a future event described in the future)
• They will say that John is to leave tomorrow. (a future event described in the future)
• They will say that John is leaving tomorrow. (a future event described in the future)
• They will say that John will be leaving tomorrow. (a future event described in the future)
• They will say that John is to be leaving tomorrow. (a future event described in the future)
• They will say that John was to leave tomorrow. (a future event described in the future)
• They will say that John was to be leaving tomorrow. (a future event described in the future)

Summary

The English strategy of adding separate little words for whatever trait you want to express may seem more complicated than in Romance languages like French, Italian, Spanish, or Portuguese, but the flexibility it affords us is more combinatorially expressive in the long run.

“John is said to be going to leave for good” is the closest I can suggest. Here is relevant material from the Cambridge dictionary ...

Future: be going to (I am going to work)
Grammar > Verbs > Tenses and time > Future > Future: be going to (I am going to work) from English Grammar Today

We use “be going to” + the base form of the verb:

I’m going to take a few exams at the end of the year.

It’s going to be difficult to get a job during the summer as the tourist industry is suffering from the economic downturn.

Cambridge dictionary

John is to leave for good it is said, would be my first thought. Although, it is not natural in my head.