I highly doubt Microsoft will release and support Linux/OSX/iOS/Android API bindings.
What will likely happen is Microsoft will :
* open source the core libs
* open source the JIT
* make sure it works on all platforms
* open source the ASP.NET and port it to Linux/Mac so they can separate Azure from being a Windows only cloud service
Xamarin then packages these in to Mono and Xamarin.iOS/Android providing a layer on top of MS core stuff. Microsoft will then be able to sell .NET as a truly cross-platform solution and make VS/Azure more popular where it's probably losing to other OSS ATM.