Irsay expects to meet with Manning in the next seven days, and the owner told The Indianapolis Star on Tuesday the return of the four-time MVP depends on his willingness to restructure his contract.
Manning has spent the past five months recovering from his third neck surgery in less than two years, and there have been conflicting reports about how much progress he has made.
The Colts owe Manning a $28 million roster bonus by March 8. They want to use the No. 1 pick in this year's draft on Manning's successor, and the future of their star QB will affect how much room they'll have under the salary cap.
Manning turns 36 in March.
"We can make it work if he wants to be here," Irsay told the newspaper. "We'd be excited to have him back and finish his career with us.
"I want him to be able to make the choice. We would love to have him back here if he can get healthy and we can look at doing a contract that reflects the uncertainty of the … healing process with the regeneration of the nerve."
The Colts went 2-14 last season without Manning, who started every game in his first 13 seasons in the NFL. He threw for 33 touchdowns and a career-high 4,700 yards in 2010, when Indianapolis went 10-6 and won the AFC South.
Manning guided the Colts to a win in the Super Bowl after the 2006 season.
The Colts also completed their coaching staff on Tuesday by hiring eight assistants and making Clyde Christensen the team's quarterbacks coach.
First-year head coach Chuck Pagano already hired Bruce Arians as offensive coordinator and Greg Manusky as defensive coordinator.