Luck, 25, is under contract for $3.4 million in 2015 with a team option for the 2016 season. He has led the Colts to the playoffs in each of his three seasons as the team's starter.
It was reported earlier this year that the two sides were working on a deal to make him the highest-paid player in the league, but Irsay said talks will not start until next offseason.
"Not right now," Irsay said. "I think that'll be a focus of next offseason that we'll address. Andrew still has two years left, and whatever our talks are between Andrew and his people will remain confidential. It's not like we don't have conversations about a possibility, so to speak, of something. But I really think most likely the scenario is most likely going to be going into the offseason next year is when that second contract will come up. That's the vision I have right now."
Last season, Luck completed 61.7% of his passes for 4,761 yards, a league-leading 40 touchdowns and 16 interceptions. Indianapolis finished No. 3 in yards and No. 6 in scoring last year.
Last season, the Colts reached the AFC championship game before falling to the New England Patriots.
- Paul Palladino