WALTHAM, Mass. -- Celtics president of basketball operations Danny Ainge is optimistic that free agents Kevin Garnett and Ray Allen might return to Boston, but he can't be sure.

On Garnett, Ainge said it's still unclear if the free agent forward will re-sign with the Celtics, but that he expects to know before Sunday, when the team can begin negotiations with other free agents.

"We're having a conversation with Kevin, but we don't have any answers on whether he's coming back or not," Ainge told reporters at the Celtics' practice facility. "I'll know that by July 1. I'll be in communication with him and I'll have some sort of read on that and a better feel."

Ainge said he isn't rushing Garnett to make a decision, despite the fact that Garnett still is the most important piece the team needs to decide upon before they openly pursue other players.

"There's no deadline with Kevin," Ainge said. "Kevin's the only free agent we have that we can talk to now. We don't have to wait until July 1 because he's eligible for an extension, but the rest of the players we have to wait until July 1."

Ainge said he still believes Garnett isn't considering playing for another team, believing he'll either choose the Celtics or retirement.

"I think so," Ainge said. "As of right now, yeah."

As for Allen, Ainge said that he's spoken with the veteran shooting guard and believes Allen is "open" to returning to Boston for another season.

Ainge can't technically discuss a new contract with Allen until Sunday, per NBA rules, but he said he has been able to get a feel for where Allen may be leaning.

"Yeah, I think Ray's open to coming back," Ainge said. "But, listen, I don't know. I won't even get into details with talking to players other than the exit interviews and Ray was getting rehab here, and we've talked. So I have a feel of where his head is, but I'll know more in July."

Allen, who's reportedly been linked to several other teams, including the Miami Heat, underwent surgery to have bone spurs removed from his right ankle June 13 . While the rehab period gave Ainge extra time to speak with Allen, he said they hadn't talked about a new contract.

"I have had conversations with Ray, yes," Ainge said. "Not contract-specific, but just sort of what his hopes and future [are], what he thinks about our team and would he like to come back and all those types of things. But I haven't had any more specifics, and on July 1 we'll talk more to Ray."