Rodgers exited Sunday's 40-33 loss to the Philadelphia Eagles in the third quarter with a rib injury, undergoing examination at the game, before a further MRI on Monday.
The four-time NFL MVP was bullish after the game about playing in next Sunday's game with the Chicago Bears. LaFleur was hopeful too on Monday following Rodgers' additional scan.
"Sometimes there's stuff that doesn't show up on all the scans," LaFleur told reporters. "All I can tell you is he's feeling a little bit better… we'll know more in the next couple of days."
Rodgers has been playing with a broken thumb on his throwing arm for the past six weeks, with his latest knock for a side with a 4-8 record prompting talk he could be shut down for the season.
Packers backup QB Jordan Love came on in the fourth quarter against the Eagles and threw 113 yards on six-of-nine passing including one touchdown in a bright cameo. Shutting down Rodgers would offer Green Bay a chance to give Love more experience.
However, LaFleur insisted that Rodgers would play if he is healthy and that he was not thinking beyond the next game.
"We've not even gone down that road," he said. "I don't think that's what we're arguing here.
"It's just, we've got a lot of faith, quite frankly, in both those guys. But you know, Aaron's the starting quarterback. He's battled through a lot throughout the course of his career. It's pretty well documented.
"I think he's been able to play at a pretty high level through a lot of different situations. So again, we'll take it one game at a time and make the best decision moving forward."
The Packers have the bye after the Bears game, offering the potential for a few weeks' rest for Rodgers if he does not play on Sunday.
"I think all those conversations, we'll have those conversations," LaFleur said. "If that's what we feel is best, then that's what we'll do."
Rodgers has a 64.8 per cent completion rate this season, making 254 of 392 passes for 2,682 yards with 21 touchdowns and nine interceptions in 12 starts.
The 38-year-old QB's nine interceptions are the most in his career since 2010, while he has also been sacked 24 times.