According to NFL rules, the Jets would have had to secure permission from the Packers to speak with Rodgers, who remains under contract, to avoid tampering penalties.
Rodgers, who is contemplating a return to the Packers, a trade elsewhere or retirement, said last week on the Aubrey Marcus Podcast that he will "make a decision soon enough."
Packers general manager Brian Gutekunst told reporters last week at the NFL scouting combine that the team would like to have "some answers" from the quarterback by March 15, the start of free agency.
Rodgers, 39, completed 64.8% of his throws for 3,695 yards, 26 scores and 12 interceptions in 17 starts this season.
He signed a three-year, $150.8 million contract extension last March. Gutekunst said that it's "fair to say" the Packers could restructure the four-time MVP's contract, if he decides to return to Green Bay.
Rodgers is set to receive a guaranteed $59.5 million this season.
Jordan Love and Danny Etling are the only other two quarterbacks on the Packers roster for 2023. Love, the No. 26 overall pick in the 2020 NFL Draft, started just one game over the past three seasons.
Zach Wilson and Chris Streveler are the only quarterbacks on the Jets roster heading into free agency.