To make ASP run under Linux, PHP script files are saved as ASP extensions and are redirected to the PHP interpreter. So it looks like the server serves ASP files, but these are actually PHP scripts.
I have seen this done first hand, surprisingly on one of the largest asp sites on the internet today. I wont mention which it is but it is a site solely about ASP which is run on Linux which fakes the extensions to appear as if it were run on a windows box.
Shakir - it is possible. As dotster mentioned, you just need to use mod rewrite to make the files look like ASP files. Either that or make Apache treat files with .asp extensions as PHP scripts. I still don't understand why you would want to do this though.