From the outside looking in, I feel it's almost a no-brainer to trade him if you can get decent value in return. The guy is obviously miserable in LA and I have serious doubts he'll resign.
If you're Chicago, do you offer a package around Noah with the dream of a Rose/Howard nucleus?
I've got no doubt at all that Chicago would do that trade - Howard's reputation as a superstar seems to have most teams willing to take a chance on him regardless of his "issues".
If I'm LA I would do it in a heartbeat. Noah is exactly the type of player they need in LA - a guy who will play hard and put in 110% effort every night, yet doesn't need the ball in his hands to make a huge impact. He would be a perfect complement to Nash, Kobe and Gasol.
First though before I do this, I'd fire D'Antoni. Too often I think the coach is the unlucky one who takes the blame when teams fall apart, and too often I think it's unfair. In this case D'Antoni is not (and never was) the right coach for this team, and a change needs to be made. Beg and plead for Phil Jackson to come back and pay him whatever you need to, failing that even that Cleveland guy was a better coach for this team than D'Antoni. They could not have chosen a less suitable coach if they tried.
If LA signs Phil Jackson and trades Howard + MWP to the Bulls for Noah + Deng (not sure if Chigago would agree) then LA are suddenly right back in the playoff race.
Could you imagine how well a lineup of Nash, Kobe, Deng, Gasol and Noah would play? Perfect balance between offense and defense, and a group of mostly unselfish guys who perfectly complement a guy like Kobe who needs to have the ball in his hands.