Coach Pete Carroll was asked Monday if he expects Wilson to play Sunday.
"Yes," he said. "Really early to say because I haven't seen him do anything other than just convince me of that thought. He's done a very good job so far.
"What he has, a lot of guys play with, and so this is something that our trainers have been through a number of times. They know that this is really possible that he'll be fine. But he still has to respond to the work on Wednesday and Thursday, and we'll see how he gets through it."
Meanwhile, at running back, Carroll said Thomas Rawls has "a little crack" in his left fibula and will be out a few weeks.
Asked if it's something that could land Rawls on injured reserve, Carroll said, "Not at this point."
Wilson was injured in the third quarter of Sunday's game against the San Francisco 49ers. He came out for one snap but then returned for three more plays to finish a drive.
The Seahawks were up 27-3 at the time, and Wilson was pulled from the game before the next possession.
The team has a Week 5 bye, meaning that sitting Wilson against the Jets would give him additional time to get healthy.
"I think, obviously, there's a consideration for that," Carroll said on 710 ESPN Seattle's "Brock and Salk" show Monday morning. "With an extra couple weeks, it would help everybody if he could sit out for a while. They'd all get healed. But we'll see what happens. We're going to do the right thing. We're going to make sure that we're very careful."
This is Wilson's second injury of the season. He suffered a right high ankle sprain in Week 1.
If Wilson plays against the Jets, he'll likely wear a brace.
"It's about stability," Carroll said. "If he's stable enough, that's why guys wear braces with those. As long as they're stable, they're fine. And there's some discomfort with it. But he doesn't feel any of that. So that's not going to be the issue most likely. It's just about, is he really stable and safe to go ahead and play? And the brace will help him with that. I would anticipate he'll be in a brace for game day. We'll see what that means."
Wilson has never missed a start in his five-year NFL career, and Sunday was the first time he had missed snaps because of an injury. Trevone Boykin filled in and completed 7 of 9 passes for 65 yards, a touchdown and an interception.
Rawls suffered his injury in Week 2 against the Los Angeles Rams. Carroll said it's unrelated to the ankle he had surgery on during the offseason.
With Rawls sidelined, the Seahawks will start Christine Michael, who carried 20 times for 106 yards against the 49ers.