Allen has a desire to continue playing alongside LeBron James, whom he developed a close relationship with during their two seasons together in Miami, whether it is with the Heat or another team. James and Allen vacationed together last week after the Heat were beaten in the NBA Finals by the San Antonio Spurs.
James notified the Heat on Tuesday that he is opting out of his contract and will become an unrestricted free agent on July 1. Both James and Allen will be unrestricted free agents. Miami's Dwyane Wade and Chris Bosh could choose to opt out as well. Neither has announced his plans.
"No news here yet," Wade said Tuesday.
Allen, who will turn 39 on July 20, played 73 games in the regular season and all 20 postseason games. He averaged 9.3 points per game on 41 percent shooting in the playoffs.
After the Heat lost in Game 5 of the Finals, Allen said he felt good about his career and had a clear mind as he faced his summer options.
"One thing is for certain, to [make a retirement decision] on my terms is the most important thing," Allen said. "Whether that is me retiring, staying here or going somewhere else, it will be on my terms. I've made it to this point, and I felt great that I have the choice to make it for myself."
Information from The Associated Press was included in this report.