At least two teams, and possibly more, have approached the Jets about trading for Wilkerson, a league source told ESPN.
More calls from teams are expected as the NFL draft gets underway Thursday night, according to the source.
Just as the Chargers don't plan to trade Philip Rivers and the Vikings don't intend to trade Adrian Peterson, the Jets don't plan to trade Wilkerson. But all of those teams are expected to listen to offers. It is up to another team to sway those clubs' thinking, which could happen in any of the cases.
Wilkerson could be the most attractive defensive player potentially available. Any team interested in acquiring him would have to weigh whether he is better than the player or players it could draft this week. Were he in this draft, Wilkerson would be considered a surefire top-10 pick, per one league executive.
At 25 years old, Wilkerson is entering the prime of his career. He also has one year left on his current contract and is seeking a new deal, which has led him to skip the Jets' voluntary offseason workouts with new coach Todd Bowles.
The contract is the issue that could ultimately lead to a trade. Wilkerson is scheduled to make $6.96 million, the amount of his fifth-year option, this season.
"To hear something that might be rumored at draft time -- this is probably my 15th year coaching, and I've probably heard everything about everybody on every team. So I can't even comment on that. Mo's on our team, and we go from there," Jets coach Todd Bowles said Tuesday.
When he recently was asked about Wilkerson's situation, new Jets general manager Mike Maccagnan did not sound overly concerned.
"I don't really want to comment on if I'd like him to be here or not be here," Maccagnan said at a news conference. "I'm sure Mo is doing a good job, wherever he is, working out. But again, these are all voluntary, so he's not required to be here for them."
Wilkerson again wasn't at the Jets' workouts Tuesday.
"I haven't spoken to him. Again, [these workouts] are voluntary. I just know that Mo's working out, and I'm sure he's gonna be fine," Bowles said.
ESPN.com's Rich Cimini and Kieran Darcy contributed to this report.