"I would love going back to those places if it worked out," Allen, 41, told the newspaper at his annual basketball camp at East Granby (Connecticut) High School, "because both teams are good, too. It doesn't necessarily have to be championship-or-bust for me to go back to the NBA.
"I want to be in a situation where I thought I could help, play a little bit and help where they have good young talent."
Allen, the fifth pick in the 1996 draft, started his career with the Bucks. He won a championship with the Celtics in 2008, then won another title with Miami in 2013. A 10-time All-Star, Allen hasn't played since spending the 2014 season with the Heat.
Boston already has an overstocked roster with 18 players under contract for next season. The Celtics do have a need for shooting and could benefit from a veteran presence given that summer signees Al Horford and Gerald Green are the oldest players on the team at 30.
Another team that has been on Allen's radar? The New York Knicks.
Longtime Knicks fan Spike Lee, who directed Allen as the lead in the film "He Got Game," has been trying to convince him to sign with New York.
"Spike Lee has been trying to recruit me," Allen said. "We've been texting."
The Knicks have 14 players under guaranteed contract and would have room to add Allen to a guaranteed contract for the veterans minimum.
Allen, an 18-year veteran, told the Hartford Courant that he would probably decide to retire if he doesn't find a situation that suits him by the start of training camp.
Allen is the NBA's all-time leader in 3-pointers made in both the regular season and postseason. In his career, Allen averaged 18.9 points and made 2,973 3-pointers in winning two championships.
According to ESPN's Chris Broussard, Allen reached out the Golden State Warriors in July about a potential return.
ESPN's Chris Forsberg contributed to this report.