Aaron Rodgers would NOT commit to playing for Green Bay in 2021 ... saying on Tuesday not much more than "we'll see" when he was questioned about his future as a Packer.

The star quarterback was in the middle of his golf round against Tom Brady at "The Match" in Montana ... when he was asked TWICE about the upcoming season.

Both times, Rodgers ducked the questions ... being as non-committal as ever about his future under center in Green Bay.

"Yeah, I don't know," Rodgers said when asked about playing against the Chicago Bears this season. "We'll see. We'll see, won't we?"

Rodgers added after being asked about the Packers' season-opener against the Saints, "I don't know. We'll see."

Of course, Rodgers is in the middle of a tiff with Green Bay's front office ... reportedly upset over his contract situation and some of the team's recent personnel moves.

The Packers have vowed to try to do everything in their power to repair the relationship ... but Aaron's icy comments Tuesday have to have the team worried.