Danny Ainge says he has had conversations with Ray Allen about Allen’s future, and — despite a report saying Allen is leaning toward signing with the Miami Heat — believes the sharp-shooter is still open to a Boston Celtics return. (ESPN Boston)

“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.”

“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.”

Allen has said his biggest concern this summer is job security. He doesn’t want to be mentioned in trade rumors every week or two, and he definitely doesn’t want to re-live what happened at the 2012 trade deadline, when he was reportedly told to pack his bags before ultimately going untraded and remaining with the Celtics. In mid-April, Allen was asked by the Boston Herald how he would react if Ainge offered him a one-year deal this summer.

“I wouldn’t be surprised,” he said of the scenario. “But I don’t want to go into this season, like I have in past seasons, worrying about whether I was going to be traded or not. At this point we want to ride it out, take this thing to the house, and not have the instability of not knowing whether today or tomorrow something is going to happen.

“For all of us, you deal with that over the course of your career, but wherever I end up after this summer, that has to be the No. 1 mandate. At this time I owe it to my family to be ultimately selfish, because I’ve been a very unselfish team player, and I’ll always do that. But when it comes to myself and my family, I have to make sure that I don’t rock their worlds or put them off kilter in any fashion.”

Do the Celtics have any chance to keep Allen? If he values stability more than anything else, probably not. Ainge isn’t likely to stop fielding offers for any of his players, especially considering that the 2012-13 Celtics could very well remain in a state of limbo between rebuilding and maintaining status quo. The Celtics’ best chance of keeping Allen is to convince him that his history with the team is worth a little uncertainty regarding where (and when, and if) Ainge will send him packing. That, or overwhelm Allen with money, since most teams likely to pursue the two-guard won’t have as much cash to spend as Boston.