The New York Jets have inquired with the Green Bay Packers about Aaron Rodgers' availability, sources told ESPN's Jeremy Fowler on Sunday.

The Jets have said they are in the market for a veteran quarterback this offseason. In addition, the Jets hired Nathaniel Hackett -- Rodgers' former offensive coordinator with the Packers -- as their offensive coordinator.

Rodgers, 39, said on "The Pat McAfee Show" last week that he is going on a four-day/four-night darkness retreat this week, during which he plans to contemplate his playing future.

"I've got a pretty cool opportunity to do a little self-reflection in some isolation," Rodgers, a four-time NFL MVP, said. "And then after that I feel like I'll be a lot closer to a final, final decision."

Rodgers, who has spent his entire 18-season career with the Packers, said he has not decided whether he will play in 2023, be it with Green Bay or another team, amid reports that he could be traded.

The Jets are in the market for a quarterback after Zach Wilson's continued struggles this season. The 2021 No. 2 overall pick has completed just 55.2% of his passes in 22 starts, with 15 touchdowns and 18 interceptions, in two seasons. The Jets have said they are committed to developing Wilson behind a veteran quarterback, however.

Jets owner Woody Johnson said after the season that he believed adding a proven quarterback would be the "missing piece" to help end the Jets' 12-season playoff drought.

Johnson, in a red-carpet interview with ESPN's Dianna Russini before the NFL Honors awards show Thursday, reiterated the Jets' desire to acquire a veteran quarterback. Johnson said the Jets' "weakness was in the quarterback position" but was careful not to mention Rodgers by name to avoid tampering charges.

When asked directly about Rodgers, he said, "I can't really talk about him because he's a member of another team, but everybody recognizes talent when they see it."

Hackett, who was fired as the Denver Broncos' head coach during his first season in the job, was the Packers' offensive coordinator for three seasons (2019-21). Rodgers said in a recent interview with "The Pat McAfee Show" that he "really bonded" with Hackett during his time with him.

Rodgers is due $59.5 million in guaranteed money this year and another $49.25 million in 2024. Of the guaranteed money owed to Rodgers in 2023, $58.3 million of it is structured as an option bonus. The window to exercise that option is from the first day of the new league year (March 15) until one day before Green Bay's regular-season opener in September.

By including that option bonus in Rodgers' contract, both sides have more than enough time to find a trade partner. Once the option is exercised, Rodgers' cap number for 2023 would be $31,623,570. Rodgers said recently on "The Pat McAfee Show" that he would be willing to adjust his contract if he decided to play next season.

Packers president Mark Murphy also talked to Russini on Thursday and said he understands that Rodgers will need to take his time before making a decision on his future.

"Obviously, he's meant so much to us. First-ballot Hall of Famer, we know he needs time. Especially when you play as long as he has, it's a grind to get ready for the season. We want to make sure that he makes a decision that he's comfortable with. So, we'll give him time, but that said, we do have to plan," he said.

The Packers also have to decide on quarterback Jordan Love's fifth-year option that would be worth roughly $20 million fully guaranteed by May 1.

Love flashed in mop-up action in a game against the Philadelphia Eagles this season, completing 6 of 9 passes for 113 yards and a touchdown, and he would be the Packers' likely starter in 2023 if they traded Rodgers.

ESPN's Rich Cimini and Rob Demovsky contributed to this report.