The Heat will only have the $3 million mini mid-level exception to offer Allen, but also have other pulls, like the chance to play alongside LeBron James and contend for titles every season.
Miami likely can't offer Allen as much playing time as many other teams, considering that Dwyane Wade plays the same position. But Windhorst reports that head coach Erik Spoelstra is likely to play James at power forward more often in the future, likely opening up more time for Allen should he sign there.
The Boston Celtics can offer Allen significantly more money than the Heat, since they have his Bird rights and can go over the salary cap to re-sign him. But the 36-year old has stated that stability is one of his top priorities in finding his next team, and Danny Ainge has included Allen in trade discussions several times over the past few years.