Gibson said he does not yet know what Hudson's options are.
"There's interesting turns in everybody's journey, and I think he'll be up to it," Gibson said. "I'm not sure where his decision process is, but we'll all certainly support him in whatever he decides to do.
"He's got a lot on his mind I'm sure. … He's an extremely driven guy, he likes to do what he does, and I'm hoping he decides to stick it out, resolve it and get back and play the game."
The D-backs expected Hudson back this month in what would have been a welcome addition to a rotation in mild disarray with Ian Kennedy and Wade Miley struggling lately and Brandon McCarthy sidelined with a shoulder injury. Now, Hudson will likely be out for at least another year, probably requiring another Tommy John procedure.
"I know he's pretty crushed about it," Gibson said. "Everything was done properly by all parties, and certainly he did his job and it didn't work out."
The 26-year-old Hudson struggled early last season before the injury, finishing 3-2 with a 7.35 ERA, but in 2011, he went 16-12 and had a 3.49 ERA with 169 strikeouts and 50 walks as the No. 2 pitcher in the D-backs' rotation.
Hudson is being paid $518,000 this year and becomes eligible for arbitration in 2014.