Is it possible to share Session object between ASP.NET (4.6) and ASP.NET CORE

Hi all

I'm working with a Webforms app (framework 4.6.2)  and the idea is to migrate to ASP.NET CORE. Before this we need to think how we can share the session between both platforms. Now I'm using SQL server to store WebForms and CORE session but the object it's completely different, different behaviour etc... Has anyone worked in some way to share the session (maybe with some middleware) betweeen both platforms?

Thanks