Allen, the NBA's all-time leading 3-point shooter, turns 39 on July 20. He averaged 9.6 points and made 1.6 3-pointers per game last season for the Heat.
The Heat and the Cleveland Cavaliers are among the teams interested in the 10-time All-Star, who won two NBA titles with Boston and Miami.
In late May, Allen admitted that retirement was a possibility.
"Do I want to get to the point where you tell me, 'Look man, you ain't looking good out there?'" Allen said. "Do you want to get to that point and people start saying that about you?
"When Barry Sanders retired, we were all like, 'What?' He only played 10 years. We wanted him to play more. But he left on his terms. He was great. Ten was probably early. But you don't want to get to the point where you are on a downside and everybody's like, 'You don't seem like you have it anymore.'"