He'll be staying a while yet. He loves Japan and lives there full time. He's just been rocketed to the top of the card, and he's not going to be giving that up any time soon.
But him being offered contracts by WWE is a non-story. WWE try and sign people all the time, especially ones who are good at wrestling. Omega is in a place where he can easily decline, and he's going to be more valuable going forward. He's no reason to sign right now. But I'm 100% sure he'll be in the WWE at some point down the line, they'll end up throwing a big contract at him at some point.
But something to note, his billed weight is 203 lbs...