Does this double negative make any sense? [closed]

Yes, both sentences make sense, although they are written in "legalese," which can make them difficult to understand.

The first,

There is a legal basis to not extend offer of employment

means there is a legal deficit, conflict of interest, lack of proof of being a member in good standing of the state's Bar Association, record of a felony conviction, or other problem based in law or applicable regulations that keeps the applicant from being considered for employment by your firm.

The second statement,

There is no legal basis to not extend offer of employment

simply means the opposite of the above: the applicant has no legal or regulatory deficits that would be a basis for not extending an offer of employment if the applicant is otherwise qualified.

It is important to note that only the first example creates any sort of obligation for your firm; i.e., for legal, documentable reasons, you cannot employ the applicant.

The second example only affirms that your firm has no basis in law for excluding the applicant from consideration for employment. This does not in any way obligate the firm to hire the applicant, who may be passed over for other perfectly legal reasons, such as the availability of more qualified applicants. As such, the apparent double-negation in the structure of the second example does not exist, although it is understandably confusing.

Yes, it's saying that you are forced, legally, to extend the offer of employment, because there is no legal basis for doing otherwise.

When we say that there is "no legal basis" for doing something, we mean that we cannot do it without breaking the law in some way. It's like saying that there is no legal way to do it.

Whether or not this actually makes sense in context is a different matter. It's saying that if you didn't offer the person in question a job you'd be breaking the law. This may or may not be what you intended to say.

I'd also add that this sort of sentence tends to confuse people, or at least make them re-read the sentence a few times to make sure they understood it correctly.