The Colts face a March 8 deadline for a decision on Manning. They owe him a $28 million option bonus on that date. If they don't pay it, he becomes an unrestricted free agent.
However, Irsay told reporters Wednesday that the two sides could strike a deal to delay the payment and the deadline.
"Look, anything is possible if the two parties choose to get together," Irsay said when asked about redoing Manning's $90 million contract.
Manning, in an interview with ESPN's Trey Wingo on Tuesday, said he plans to continue playing football and that his recovery from spinal fusion surgery in September -- his third surgery in 19 months -- is going well despite the fact he didn't play last season.
"I really feel good. I continue to make progress every day," he said. "Everything that the doctors have told me has been on point, which is encouraging to me. I just had a great day today with rehab, just got back from the facility, and that's what we continue to do. Just keep trying to get better. So far I have. That's the plan from here on out."
Manning also said that he'll continue to have checkups over the next several weeks, and termed his mood as "encouraging."
Irsay said Wednesday that he will take into account both Manning's short-term and long-term health.
"It's two-phased. There's the medical aspect, as to whether he can play at a really high level and that's the only place he wants to be. Can he drill it in Foxborough in 10 degrees, 50 yards, that sort of thing," Irsay told a small group of reporters. "The second issue has always been his health and the risks of going back onto the field. When the Super Bowl ends, he and I will continue to talk about it."
Irsay said that the lack of precedence with Manning's injury clouds the decision process.
"There's so much uncertainty in this thing," Irsay told NFL Network on Wednesday. "The thing that gets overlooked in situations like this, is that there's never been an NFL quarterback that has had this type of injury. It's never happened before. When our doctors talk to other doctors, even throughout the world, the reference points just aren't there. This will be a case study, if it ever happens again, because it's so rare that you have this situation.
"You try to work through the uncertainty, but that's been the tough part about this."
Irsay also said that while money is not an issue, he doesn't want to make a decision that will hamstring the team's salary cap in future years.
"If it helps us win, I'll pay it in a second. But when it comes to salary cap ... we have real cap problems," Irsay told NFL Network. "You can't make a decision that straps you for the next three seasons.
"If we make a decision based on just affection, and we have cap problems for three years, the fans will call me an idiot."
Earlier Wednesday, new offensive coordinator Bruce Arians said he hopes Manning returns to the Colts though he believes the best way for a rookie quarterback to learn is by playing. He didn't drop hints about the Colts' plans for Manning or what Indy would do with the No. 1 overall draft pick.
Irsay has already said the Colts will choose Manning's successor in April. The decision is expected to come down to presumed No. 1 choice Andrew Luck or Heisman Trophy winner Robert Griffin III -- either of whom would get playing time if Arians has a say.
Irsay reiterated a point Manning made Tuesday, saying that no decision has been made yet.
"People assume that the people know what they're going to do and just aren't telling us," Irsay told NFL Network. "Often times, you don't know, and take as much time to be thoughtful and make the decision at the last possible moment you can. It's not true that any decision has been made. I wouldn't say it's a certainty that it will go one way or another.
"No one knows what is going to happen."
Information from The Associated Press contributed to this report.