MonoGame is an open source framework taking over as XNA dies.
MonoGame will be getting PS4 support soon
From MonoGame’s side people have actually already acknowledged how good libgdx is and wrote code and made guides like this: Port a 2D libgdx game to MonoGame
While this is a possibility I am seriously considering, it would be much nicer of course if there was a direct backend.
Since libgdx is very popular and everyone wants a route to PS4, this seems… not that bad.