Luck has been in Europe since last month to receive treatment on his surgically repaired shoulder.
"He's doing great," Irsay told NFL Network. "He's doing well. [We're] disappointed, obviously, it's taken as long as it's taken. You know, medicine and the way it goes. But there hasn't been any unusual setback. We didn't find out anything ominous, something we didn't know about or anything like that. It's just taken time for him to go through his whole aspect of rehabbing and progressing and working through the soreness."
Irsay added: "No additional surgery at this point [is] planned."
The Colts placed Luck on injured reserve Nov. 3, ending his season. The decision came after Luck visited with doctors to ask why he was still having soreness in his right shoulder. It also ended months of speculation about whether the quarterback would play this season after having surgery in January.
Luck originally injured his shoulder during the 2015 season, in Week 3 at Tennessee. He missed two games due to his shoulder and then missed the final seven games of that season due to a lacerated kidney. Luck missed one game last season with a concussion and all of this season with the shoulder injury.
Despite dealing with the shoulder injury that caused him to miss practice at times last season, Luck threw for 4,240 yards and 31 touchdowns while completing a career-high 63.5 percent of his passes.