Parker’s agent, Henry Thomas, confirmed the talks but he said a meeting has not been scheduled.
Training camp and the free agent signing period opens Friday, and the Celtics have just six players under contract.
Ainge has also expressed interest in free agents Shannon Brown, Kwame Brown, Marquis Daniels, and Reggie Evans as he looks to fill out the roster. He’s also talked to representatives for Glen Davis and Delonte West.
The window to put a roster together is small. The Celtics open Dec. 25 against the Knicks at Madison Square Garden.
When Daniels went down with a bruised spinal cord last February, the Celtics were rumored to be interested in the 6-foot-6-inch, 210-pound Parker.
When Cleveland signed Parker before the 2009 season to put a shooter and defender around LeBron James, Celtics coach Doc Rivers said it was a more impressive offseason move than the Cavs signing Shaquille O’Neal that same summer.
Parker, 36, averaged 8.3 points, 3 assists, and 3 rebounds in 72 games for a hapless Cavs team last season.
The Cavaliers would like to resign Parker, and the New York Post reported the Knicks are also interested.
Rondo is ready
Players were allowed to come to team facilities yesterday for physicals, and Rajon Rondo passed with no red flags.
The gruesomely dislocated right elbow he sustained in Game 3 of the Celtics’ second-round series against the Heat seems to be fully healed. He showed no ill effects last month at his charity game at Harvard.
“I think he’s been ready to go for months,’’ Ainge said.
Although he averaged a career-high 37.2 minutes, Rondo, 25, played a career-low 68 games last season, missing time with ankle and finger injuries.
Rondo worked out yesterday in Waltham for the third time since players were allowed to use the facilities. Avery Bradley and JaJuan Johnson were also in attendance.
Schedule out tonight
The league will announce the 2011-12 schedule tonight at 7 on NBA TV.
What’s already known is that the Celtics open Christmas Day, the first game (noon start) in a five-game showcase.
The Celtics will play the Heat at Miami Dec. 27, CSNNE reported, and the Los Angeles Times reported the Lakers will come to Boston as one of their 18 nonconference games.
Julian Benbow can be reached at jbenbow@globe.com.
