All three players will count toward the team's 90-man roster heading into camp.
Geathers is expected to miss the start of the regular season with a neck injury. Hooker tweaked his hamstring on Monday, according to Colts.com. The Ohio State product had shoulder and sports hernia surgeries in January.
"Andrew's got to work on getting his throwing motion back, all his strength back," Colts general manager Chris Ballard told reporters Monday. "Andrew has not had any setbacks at all in his rehab process or with his surgery. He is in good shape; he's in good standing. Long term, his shoulder, the prognosis is very good and that's very positive."
"We're going to continue to follow the doctor's orders and the rehab process. This is a process. We've not put a timetable on this for a reason. There's a process with his rehab and his health and long-term success."
Luck, 27, had offseason shoulder surgery but is expected to be ready for the Colts' Week 1 matchup on Sept. 10 against the Los Angeles Rams at Los Angeles Memorial Coliseum.
The former No. 1 overall draft pick has had issues with the shoulder since 2015. He later suffered a lacerated kidney.
Luck signed a five-year, $122.7 million contract last offseason. He resumed throwing the football about a week ago, according to the Colts' website.
The Colts also put Kendall Langford and Brian Schwenke on the Active/PUP list.
Luck, Hooker and Geathers can be removed from the list at any time. Although the Colts would not disclose a timeline for Luck's return, Ballard sounded as though he didn't think the preseason was necessary for Luck.
"I'm comfortable when our doctors and our trainers clear him and say he's ready to play," Ballard told reporters. "Whether that means he plays in preseason or doesn't play in preseason, that's up to our doctors and trainers to tell us where he's at and for Andrew to tell us where he's at."
Luck had his career-best completion percentage last season (63.5) and threw for 4,240 yards, 31 touchdowns and 13 interceptions. In 2014, he led the NFL with 40 touchdown passes, while completing 61.7 percent of his throws for a career-best 4,761 yards.
Colts players report to camp on Saturday.