The Minnesota Timberwolves may be looking to make a deal before the NBA's trade deadline, which arrives at 2 p.m. Thursday.
According to Yahoo Sports, NBA sources say the deal is still fluid.
KSTP-AM reports Allen has been sidelined for the past 20 games because of a ligament injury to his hand, but he is listed as a game-time decision on Tuesday when Memphis hosts the New York Knicks.
Allen has averaged 10.2 points and 3.9 rebounds a game in 27 games this season. According to the Yahoo report, he would bring the Wolves a defensive toughness that Wolves president of basketball operations Flip Saunders has been looking to add.
The Grizzlies have been trying to unload Prince and the remaining $7.2 million left on his contract this year and $7.7 million next year.
Budinger has missed much of the early part of the season for the Wolves as he recovered from knee surgery. He has averaged six points in just over 17 minutes per game since returning. Barea is averaging 8.7 points in 18 minutes per game this season.