Rodgers and the Packers are at odds over the team's selection of a quarterback in the first round of the 2020 NFL Draft. A contract dispute also continues.
"Knowing Aaron, and I think I know him fairly well, if he has a grudge, whether it be against the organization or a player or an arch rival, family, friends, he ain't budging," Favre said Tuesday on the Bolling with Favre podcast.
"I don't see him coming back if this is not resolved, whatever the issue is. Even if it's resolved, but he feels like they have one up on him, he ain't going to play. Knowing Aaron, he would sit.
"He would forgo a lot of money, but he's got a lot of money."
Sources said last week that Rodgers told members of the organization that he doesn't want to return to the team in 2021. Packers general manager Brian Gutekunst told reporters Thursday that he will not trade Rodgers.
The Packers have offered to extend Rodgers' contract several times, but the future Hall of Famer has declined a new deal.
Favre once faced a similar circumstance to the one Rodgers faces. Favre spent 15 seasons as the Packers' starting quarterback when the team picked Rodgers in the first round the next off-season.
Favre was 37 years old at the time. He was traded to the New York Jets the next off-season.
Rodgers played his 15th season for the Packers before they picked Jordan Love in the first round of the 2019 NFL Draft. He is 37 years old.
Rodgers completed a league-best 70.7% of his throws for 4,299 yards and a league-best 48 touchdowns and just five interceptions in 16 games last season.
He signed a four-year, $134 million contract extension in 2018. His salaries are to be $22 million in 2021 and $25.5 million in 2022 and 2023.
"The fact we're in this spot is certainly not what I want, especially when you're talking about the league MVP and all the great moments we've had together," Packers coach Matt LaFleur told Packers.com on Saturday.
"Hopefully we will resolve this and he will be back in a Green Bay Packer uniform."