"Cash on me" vs. "cash with me"

Solution 1:

Both are grammatical and both are found, but cash on me is probably more frequent in speech.

Solution 2:

As Barrie England suggests, cash on me is probably more common in speech, but cash with me would have a slightly broader meaning. Cash on me would mean cash about my person, in my pockets, boots, wrapped in my handkerchief, or something of that nature. Cash with me might also include in my suitcase, in my car or caravan, or anywhere else near to hand but not necessarily about my person.

Solution 3:

Grammatically, I think both are correct.

I don't have any cash with me.

Seems all right to me, since people also use,

I haven't brought the cash with me.

I'll try to find some reference to the usage on the internet or my Oxford Dictionary.