Rodgers was believed to be targeting Dec. 24 as a potential return from a torn Achilles -- only 3½ months removed from surgery -- but he wouldn't rule out an earlier comeback.
"Anything is possible," he said Thursday in an off-camera interview with beat writers.
This doesn't mean his return is a sure thing. Rodgers made it clear that the Jets (4-7) need to be alive in the playoff race. He also emphasized that he needs to show considerable improvement next week in practice.
"It feels great to be on the practice field, but I'm not anywhere near ready to play," said Rodgers, who was cleared Wednesday for limited practice.
He's hoping he gets some cooperation from teammates. Losers of four straight, the Jets have less than a 1% chance of making the postseason, according to ESPN Analytics. If they lose Sunday to the Atlanta Falcons (5-6), it could be a moot point.
"I don't think that would make a ton of sense," he said, meaning to play in a game with no playoff implications.
"A comeback this year before the four-month mark would mean I'm not 100 percent healthy, so it'd be a risk for myself. For the team to sign off on if we're out of it, I'd be surprised if they would OK that to come back."
Rodgers, who turns 40 on Saturday, reiterated his desire to play in 2024. A reinjury this season wouldn't change that, he said.
After a limited practice Wednesday, during which he took some reps in 7-on-7, Rodgers sat out Thursday as part of his rehab plan. That will change next week, when he tests himself by practicing on back-to-back days.
"Obviously, Sunday [is] out of the question [to play], but I'm going to push it next week, see how I'm feeling after Monday, Tuesday, Wednesday, Thursday and see how I respond," he said.
He confirmed that he had been targeting Christmas Eve against the Washington Commanders as a potential return, but he said his rehab is progressing so well that he decided to return sooner than expected to practice.
But he was quick to note that he still has a lot to accomplish in practice before he's game-ready.
"Obviously, I can drop back, I can do some things in a small circle, but I don't think I can protect myself as well as I'd like to at this point," he said. "So I've got to do a little more. In practice, I have to take live team reps [in 11 on 11]."
Whether he plays or not, Rodgers has staged a remarkable comeback. He was injured Sept. 11 on the fourth play of the season and underwent surgery Sept. 13. No NFL player has returned from an Achilles tear before five months. He admitted he's motivated, in part, to do something unprecedented.
He was told by many medical experts that it couldn't be done. Asked why he's trying to return so quickly, Rodgers gave an incredulous look to a reporter.
"Why? Do you know my history?" he asked. "It's never been, 'Why try?' For me, it's, 'Why not?'"
Without Rodgers, the Jets are experiencing an abysmal season on offense, fueling speculation about the future of general manager Joe Douglas, coach Robert Saleh and offensive coordinator Nathaniel Hackett. Asked if his future is tied to this group returning in 2024, Rodgers said, "I think that's such a trap question."
He said he doesn't make those decisions, but it's obvious that he wields considerable influence within the organization. Rodgers did say the Jets "have a really good organizational structure," praising Douglas, Saleh and Hackett.
"I feel like the recipe's in place to be really successful," he said. "Whether it's finishing up this year or starting for us next year, I feel like with those guys in position of leadership, this team can get to where it wants to go."