There was a post on http://www.MoDB.CoM/Engines/XNA/ (Maybe it’s time to add MonoGame?) showing XNA inside of Unity3D, found here: http://www.GitHuB.CoM/MVI/UnityXNA
Obviously not the most ideal situation, but it seems like an interesting approach to put your games on platforms XNA/MonoGame are not on yet, if ever… With the added benefit of being able to use Unity3D and their asset store. Possibly even being able to sell your XNA/MonoGame code/assets, as neither Microsoft or MonoGameTeam have a store setup for that.
I actually thought about this few days ago(when Unity was released on Linux), and I did manage to get my minigame working. The bad side to this is that Unity uses an outdated version of C# so I had to modify part of my code.
Once they update their C# version I’ll look into actually creating a MonoGame port for it.
I also did a version of a MonoGame inside Unity project here:
It is a terrible idea and a big hack, but it was good enough that I could enter (and win) a unity competition with my “unity powered” game 
Yeah, it is a bit of a crazy idea. A Friend of mine decided to also hack a similar approach with XNA
Main problem is that Unity and XNA/MonoGame are poles apart for how they build a scene to render.