can write an AIR app that
accesses those ASP pages. AIR/Flash/Flex come with several
classes for accessing web services. If your site isn't already
factored out to provide generic web services, it's a good thing to
do anyway. Then your ASP pages and your AIR app both get their data
from the same source. This also lets you choose to open up the API
you've created to outside users, potentially increasing the
popularity of your site.
I may have been taking the question to literally...
There is absolutely no way to take your website in ASP and
directly put it into Air. You can, however, create a webservice and
make calls against it and write an Air application that interfaces
with your website as stated above.