A preinvitation is a presequence that is likely to be understood by the respondent as a signal of a coming invitation. The coming invitation may be a question-answer sequence concerning the availability of the participant to be invited.
The second and third turns of the following exchange are a preinvitation:
Levinson, Stephen C. 1983.Pragmatics. Cambridge, England: Cambridge University.
Atkinson, J. Maxwell, and Paul Drew. 1979.Order in court. Oxford Socio-Legal Studies. Atlantic Highlands, NJ: Humanities.