No. Your best bet might be to use something like cookies.
Unless there is no other way for your problem, I would suggest not mixing
code environments. The reason being that ASP and ASP.NET are handled by
entirely different execution engines. You run into a lot of problems as one
group of pages does not know that the other exists. Because they use
different engines, the do not share memory space. This can lead to logical
inconsistencies. Suppose that a user accesses your home page, which might
be ASP.NET. A session is started. Now, they navigate to another page that
is ASP only. A second session is started, even though logically the user is
in the same web application.
I think this is how things work.