WALTHAM, Mass. (AP) — The Big Three of the Boston Celtics very well could stick around beyond their current contracts with a changing cast of supporting players.

Ray Allen will be 34 after the one year left on his contract, Paul Pierce will be 33 after his two remaining years and Kevin Garnett will be 36 after the three years left on his deal.

General manager Danny Ainge was enthusiastic Wednesday about the idea that they might stay longer than that if they are healthy.

“Absolutely, no question,” he said. “If they take good care of themselves, which all three of them do, and they stay healthy I think there’s a really good chance. I think all those guys will be up in my office pretty quick looking for more years on their contracts.”

Ainge also said he planned to address the contract situation of point guard Rajon Rondo this summer after handling more pressing matters that came with the start of the free-agent signing period Wednesday. Rondo will make $2.62 million next season, and the Celtics can make a qualifying offer after 2010-2011 to make him a restricted free agent and allow the team to match any offer he receives.

Glen Davis, a solid replacement when Garnett missed much of the second half of the season and all of the playoffs with a knee injury, plans to seek free agent offers that the Celtics will have a chance to match.

Backup forward Leon Powe was allowed to become a free agent and isn’t expected to return. He could miss more than half the season following surgery for a serious knee injury in the playoffs.

Substitute guard Eddie House, an effective 3-point shooter, decided to fulfill the last year of his contract for $2.86 million rather than exercise his option to become a free agent.

The Celtics had no first-round pick this year after trading it to Minnesota in the Garnett deal before the 2007-08 season when they won their 17th NBA championship.

They chose guard Lester Hudson of Tennessee-Martin with the 58th pick of the 60-pick draft.

“Every year there’s players picked at 58 and … they rarely do make it,” Ainge said. “I think Lester has the opportunity of a lifetime that a lot of people would like.”

Hudson, who once had a quadruple-double in points, assists, rebounds and steals, thinks the fact that he’s 24 and that he grew up in a tough neighborhood will help.

“I’m more mature, can handle a lot of stuff that’s thrown at me,” said Hudson, the NCAA’s second leading scorer last season. “I’ve been going through a lot over the past couple of years, a lot of bumps and bruises in my life, so I think they help me out a lot.”

The Celtics greatest need is a forward who also might be able to back up center Kendrick Perkins. Among available free agents Ainge is interested in are Rasheed Wallace from Detroit, Grant Hill from Phoenix, Marcin Gortat from Orlando and Zaza Pachulia from Atlanta.

“We know that probably the whole pool of money for free agents isn’t going to be what it’s been in the past,” Ainge said.

Davis’ value shot up during the strong finish to his second season.

“Everything’s been pretty positive with Glen. We haven’t had negotiations,” Ainge said. “We’re hopeful that he’ll be part of our team this year.”

Powe sounded certain that he won’t be but wasn’t surprised that he didn’t receive a qualifying offer that would have kept him from becoming an unrestricted free agent. Still, he said he was disappointed after talking with Ainge on Tuesday.

“They told me, ‘Good luck with another team,’ ” Powe told the Boston Herald.

Ainge doesn’t expect him to play until late in the season.

“We’ll certainly keep tabs on Leon and see how his progress is coming along throughout the summer and maybe throughout the year if he hasn’t signed with another team,” Ainge said.

A phone call to Aaron Goodwin, Powe’s agent, was not returned.

Ainge is balancing a desire to win now with his effort to keep the team competitive if the Big Three don’t sign new contracts with the Celtics.

Five of their 11 players under contract for next season are 24 or younger. Davis is 23.

“I don’t feel like the world’s going to collapse when our Big Three are too old to play anymore,” Ainge said.