Coach Chuck Pagano said Monday he'll have a better idea of Luck's availability on Wednesday, which is the next time the team will practice.
"Andrew is progressing well, getting stronger and there might be chance," Pagano said. "He might be able to start some practice this week, but I'm not guaranteeing nothing, so don't write anything. There's a possibility.
"When our doctors and our trainers tell me that he's at a point where he can get back out there to begin to practice, then I'll be able to tell you for sure. He's doing well."
The Colts have been waiting for this moment since Luck had January surgery on his right shoulder. He missed the team's offseason workouts and was placed on the physically unable to perform list at the start of training camp. Luck was taken off the PUP list before the start of the regular season, but the team kept its stance that there was no timetable on when he would practice.
There's also not a set date for when Luck will play in a regular-season game once he starts practicing. ESPN's Chris Mortensen reported Sunday that Luck will need three to four weeks to get ready to play and a possible return game would come in Week 7 against Jacksonville at Lucas Oil Stadium, barring any setbacks.
Once Luck does practice, he'll initially get snaps with the scout team because the Colts don't want to disrupt the first-team reps Jacoby Brissett is getting. Brissett, who the Colts acquired from New England on Sept. 2, has started the past two games. He's 39-of-64 for 526 yards with a touchdown pass and an interception this season.
Brissett ran for two touchdowns on Sunday as the Colts (1-2) defeated Cleveland 31-28.