"I've shared it with some of my teammates as well as the organization as well as everyone else in Boston. If you guys will have me back, I plan on re-signing here next year," Irving said to rousing applause at an event for season-ticket holders at TD Garden on Thursday night.
Irving, 26, is entering the final year of the five-year, $94 million contract he signed with Cleveland before the 2015-16 season. He has a player option for the 2019-20 season and can become an unrestricted free agent after that.
He joined Boston in a trade from the Cavaliers last August, but his season ended in March as he dealt with persistent knee trouble.
Irving hinted last month that he would like to stay in Boston, but cited "financial implications" as the reason why he has not immediately signed a new deal.
If Irving had signed an extension with Boston this past summer, he would have potentially left more than $80 million on the table than if he waited and re-signed with the Celtics next summer.
Some reports had linked the New York Knicks with an interest in luring Irving in free agency, potentially alongside Jimmy Butler, but Irving told ESPN in September that he had not spoken to Butler at length since 2016.
"I'm accepting it's going to be a constant story," Irving said of the free-agency rumors. "It's a point in my professional career where it is a big-time decision. I've been away from Cleveland officially for a year now, and I'm finally getting acclimated in Boston."
Former Celtics great Paul Pierce told ESPN that Irving opting to return would be a smart move for his legacy.
"I think that's a legacy decision and for him to see the potential of that team moving forward in Boston," Pierce said. "Winning a championship in Boston is different than winning one in Cleveland. He will be immortalized if he wins in Boston."
ESPN's Amina Hussein contributed to this report.