"I would love going back to those places if it worked out," Allen told the newspaper, "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, 41, began his career with the Bucks and won an NBA title in 2008 with the Celtics.
Another team that's 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, who hasn't played since the 2013-14 season, is the NBA's all-time leader in 3-pointers made in both the regular and postseasons. In his career, Allen averaged 18.9 points and made 2,973 3-pointers while winning two championships.
According to ESPN's Chris Broussard, Allen reached out the Golden State Warriors in July about a potential return.