Rodgers is reportedly seeking an exit from the Packers, in large part due to a fractured relationship with the team's front office.
Favre can relate to the reigning MVP's situation, having endured a messy departure from Green Bay in 2008 that paved the way for Rodgers to take over the starting job.
The Hall of Fame quarterback said Tuesday on his podcast, "Bolling with Favre," that he believes Rodgers will retire before rolling over for the Packers.
"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 archrival, or family, friends - he ain't budging," Favre said.
He continued: "Whatever the issue is - if it's not resolved, or even if it's resolved, but he feels like they got one up on him - he ain't gonna play.
"Knowing Aaron, he would sit. Now, he would forego a lot of money, but he's also got a lot of money."
If Rodgers does retire, he'll forfeit $44.5 million, according to Mike Florio of Pro Football Talk. He would be required to repay $23 million in unearned signing-bonus money and miss out on his $14.7-million base salary and $6.8-million roster bonus for this season.
Rodgers' issues with Packers general manager Brian Gutekunst apparently revolve around the team's decision to select quarterback Jordan Love in the first round of last year's draft without informing Rodgers beforehand.
The 37-year-old is reportedly adamant about not returning to Green Bay unless Gutekunst is fired. The NFC North club's reported offer to make Rodgers the NFL's highest-paid player has apparently done nothing to change his stance.
Favre and Rodgers have become friends in recent years after a strained relationship during their three seasons together in Green Bay.