Nope, ASP and ASP.NET are totally different entities, similar in name only.

The only way to exchange data between them is either via Cookies or some backend store.

I think you can modify ASP to use a SQL Server to store session state, then share it with ASP.NET, but I don't know.

For small amounts of data, your best bet is with Cookies, but remember they're a client-side feature and cannot be trusted or relied upon