All Oden has to do this summer is leak some footage of him running up and down the court in a pickup game to get teams to throw at least a LLE deal at him.
He might want to get with an NBA team now, to use their facilities and medical staff, but is probably going to want more than a vetmin deal. There's really not much upside for the Cs to do it unless they get a contract that controls him for the rest of this season, where he probably never gets on the court, and next, where the upside is huge for a small investment.
The reason for him to sign now is simple. It makes it easier for him to get paid, and stay in a favorable situation earlier.
If he waits until the summer to sign, and only signs a one year deal, then the team he signs with would only be able to resign him to a larger contract if they used their MLE or cap space...and if he is looking to hook up with a good organization, that is close to the luxury tax, that MLE might only be $3 million.
However, if he signs now, he can play out next year, and then have early Bird rights next summer, which will allow him to resign with that team (assuming he likes it there) for 104% of the league average salary (MLE) without them having to use any exceptions.
Or if he signs a three year deal, he would have full bird rights in 2 seasons rather than 3.
Its actually a very smart tactic, and probably worth the extra couple million he might be giving up for next season, by not waiting for the summer to sign.
He is taking the longview. Find a situation that is beneficial to him, where he thinks he has the best chance to succeed, and look to cash in on a bigger contract, not this little one.