According to the Observer it's the 31st.
Dave Meltzer, for what it's worth (and he happens to be wrong A LOT) also said on Wrestling Observer Radio that people in New Japan have also indicated that Kenny Omega has already resigned a long term deal with them. So he basically covered his ass by saying both his contract may expire and may not expire on January 31. Regardless of what Kenny does, he can say he was right.
Kenny Omega is not coming to WWE anytime soon. He is not an idiot. He is the second biggest star in NJPW right now. He was the first gaijin to win the G1 Climax. That alone tells him how NJPW values his worth. He will undoubtedly be a future IWGP Champion. With his personality, if he came to WWE, he would be turned into a complete joke. Vince would likely enjoy his more outrageous behavior BUT he wouldn't take Omega seriously. If he signed Omega, it would simply be to take him from New Japan. He would likely have a good first couple months and he would become Gallows and Anderson. WWE would love to take the guy who took on NJPW's top guy and took him to the limit in what many are calling the best match ever, and make him Roman Reigns' bitch. Kenny is smart. He knows that.
So it's stay in NJPW and with a company that respects you, will pay you a lot and have you on top for likely a long time... or go to WWE, who will treat him as a joke and likely cut him loose in about two years after all their "top guys" have had their way with him.
Omega ain't going anywhere.