People keep saying this isn't possible because of strengths and how Godzilla would destroy the Jaegers, etc.
1. It's entirely possible legally as both films are produced by the same company.
2. They seem to be forgetting that Godzilla was the good guy in the recent movie. The Jaegers and Godzilla would be on the same side, like Gamera and the SDF in Gamera 2: Attack of Legion, where he could fight the big Legion and not the small ones, while the SDF could fight the smaller Legion and not the big.
Of course, Godzilla would have to take place within Pacific Rim's opening montage, or be some parallel universe, but since Pacific Rim's portal was already to another universe, that doorway is open if they wanted to get very silly.