You can't use same master pages. You can't reuse ASP.NET MVC for some parts of your webforms view and vice versa. Either your view is completely on webforms or on ASP.NET MVC. And theoretically even mix of webforms with mvc in one web application could be problematic, but practically possible (see below point 1). So generally answer to your question is no.
If you are looking to ASP.NET MVC, you should think about step-by-step migration of your project to it.
Actually there are a couple of possibilities how to migrate
Mix in one project ASP.NET web forms and ASP.NET MVC. Technically it is possible. But it is some kind of hack. Your transition will be seamless but you can't your ASP.NET views. I will not recommend it. You can find this approach here http://www.devcurry.com/2013/05/adopting-aspnet-mvc-enhancements-in.html
In one solution use different projects for your webforms and mvc projects. In fact these are 2 different web application which typically could have common authentication, and there is question with webforms state. To solve problem with authentication you need create separate web service for it, which will be used by both. To solve problems with session state, use distributed caching for both, and try to change thinking from webforms state to caching, because mvc is actually stateless. Then for particular views you can redirect between views of both portals