Rodgers said he would like to play five seasons after the 2018 season.
"I'd love to play to 40 [years old]," Rodgers told NBC Sports' Peter King. "I just think that number means a lot. Obviously, Tom [Brady] is kind of rewriting the book. Brett [Favre] had a good season when he turned 40. My goal is, be able to move like I do or close to how I do and still be able to do that at 40 ... just because nobody's been able to do that and still move around the same.
"Steve Young's career was cut short in his late 30s. John [Elway], the same -- he didn't really move the same as when he was younger. So to be able to move the same way at 38, 39, 40 would be cool. That's my aim."
Brady, who was named league MVP in 2017, turns 41 next month.
Rodgers has two years remaining on his current five-year, $110 million contract. The Packers could use a franchise tag for two seasons beyond that, but both sides have been saying they hope to get a new contract signed within the next few months.
Rodgers suggested his new contract might differ from traditional deals and could set a precedent for future contracts.
"It's only been on my mind because ... people have been writing and talking about it a lot," he said. "There have been many conversations about it. I think that there's some merit to looking into where you do a non-traditional contractual agreement. If anybody at this point is gonna be able to do something like that, I think there needs to be a conversation about it. I never said anything about [tying the contract to] the [salary] cap. I just think there's ways to do contracts where you can still be competitive so the team is happy about it, but have some more freedom."
He has come to realize that the team has the final say on a player's career.
"But I think in my time [in Green Bay], I realize no one is above the team," he said. "They can trade Brett Favre, Jordy Nelson. They cannot re-sign a Charles Woodson or Julius Peppers. They make decisions that are in the best interest of the team. It could be me at some point. You have to be humble enough to realize that, and I do. I'd love to be able to ...
"How many guys get to actually pick the way and the team how they go out? You know? Hardly anybody. You have to understand that's a real possibility. But yeah, my dream situation would be to stay in Green Bay."
Rodgers missed nine games in the 2017 season after breaking his collarbone for the second time.
The 247Sports website projected what Rodgers' career statistics might look like if he played six more seasons. His current career numbers are as follows: 65.1 completion percentage, 38,502 passing yards, 313 passing touchdowns, 78 interceptions and a 103.8 passer rating.
If Rodgers does play until he is 40 and continues to perform at his current level, his estimated career numbers would be as follows: 65.0 completion percentage, 61,404 passing yards, 499 passing touchdowns, 126 interceptions and a 103.8 passer rating.
Only five players in NFL history have recorded at least 60,000 passing yards, and only two players have thrown more than 500 career touchdown passes.
These projected statistics are based on an average of Rodgers' yearly statistics since he became a starter in 2008.