Mono (the code) and .NET Core will merge (per Scott Hanselmann)

Microsoft will (in partnership with Mono the project) ensure that .NET core and server stacks run on Linux and OS X.

They've just demonstrated deploying an ASP.NET MVC5 application on Linux, running inside a (Linux) Docker container and being remotely debugged from Visual Studio on Windows. Which seems to indicate that they are already pretty far down that road.