While Jauron said a decision wouldn't be made until Wednesday he admitted some players would get a look as the season comes to an end.
"We've got a No. 1 draft choice that hasn't played a lot. We think he's going to be a fine player. We've got two experienced quarterbacks," Jauron said of the quarterback situation. "We have three games left; we're going to do everything that we can to win these three games while we look at personnel possibly that we haven't seen enough up to this point."
Grossman, who served as backup Sunday due to Chris Chandler's sore right shoulder, said he'll be ready.
"It's not my call," he said. "But I'm going to just go to practice like I do every day," he said.
If Grossman starts, it will be the fourth time in Jauron's five years that the third-string quarterback started a game.
Jauron has said in the past that Grossman wasn't ready to be a winning starting quarterback on a consistent basis.
"He's gotten better each week on the practice field," Bears offensive coordinator John Shoop said after Sunday's game. "He's gotten better each week in the meeting room and has gone about his business professionally.
"I know he's anxious to play, but it's really difficult to say exactly where he is until he gets out there on the field. What he has done to this point has been positive and he has been getting better and we've been working with him with a sense of urgency."
Jauron had said in the past that Grossman would be considered once the team got eliminated. Starter Kordell Stewart went 17-of-40 for 256 yards, but had little to say about the possibility of being benched now that the Bears are mathematically out of it.
"That's my last concern right now as far as mathematically and Grossman and all that stuff," Stewart said.
Grossman's only action so far has been in preseason, when he completed 28-of-56 for a team-high 287 yards with one touchdown, two interceptions and a passer rating of 56.2. He has been active but did not play five times this season.
Some players may want to finish strong to try and save Jauron's job. Whether Grossman will give them the best chance at that remains to be seen.
Regardless, they may have bigger concerns of their own to say much.
"When you lose football games, players and coaches are the same," defensive tackle Bryan Robinson said. "You don't know who is going to be around, so you fight until the end and you just pray to God that you're not the one who's going to be out of here."
Mike Gandy was the only player that came out of the game against Green Bay banded up. He had an MRI on his left shoulder and everything checked out okay according to Gandy.