I don't see any obvious relationship. However, I am currently reading an article in Language in Society that links use of "do you want..?" vs "wanna..?" to the speaker's perception of the listener's willingness to accept the proposition. So there could well be a relationship that has not been systematically explored.

The other classical theory of speech acts is intentionalism, which Paul Grice began to develop in parallel to Austin’s views while they were both at Oxford in the 1940’s. The central claim of intentionalism is that performing a communicative illocutionary act is a matter of producing an utterance with a special sort of intention, normally called a ‘communicative intention’, a ‘meaning intention’, or an ‘m-intention’. The nature of communicative intentions is a matter of debate, but the crucial idea is that performing a communicative act is a matter of producing an utterance intending both (a) for one’s addressee to have a specified response, and (b) for one’s addressee recognize to that this response is intended.