Shams Charania of The Athletic and Stadium noted the Celtics will be using their $4.8 million room exception in an effort to upgrade their frontcourt depth this summer.
Boston is set to undergo a roster overhaul during the offseason with point guard Kyrie Irving, center Al Horford and power forward Marcus Morris all on their way to the open market.
The expected changes come after the Celtics entered the campaign with championship aspirations only to secure the fourth seed in the Eastern Conference and get eliminated by the Milwaukee Bucks in the second round of the playoffs.
Charlotte Hornets point guard Kemba Walker, one of the summer's most coveted players, is the team's expected top target when the free-agent market opens. ESPN's Adrian Wojnarowski labeled the C's as the "front-runners" to sign the three-time All-Star selection on Thursday.
Boston will likely attempt to finalize the Walker deal before shifting its focus to potential second-tier options like Kanter and Looney.
Kanter averaged 13.7 points and 9.8 rebounds while shooting 54.9 percent from the field across 67 appearances split between the Blazers and New York Knicks last season. His deficiencies at the defensive end led him to rank 52nd among 64 qualified centers in ESPN's Real Plus-Minus, though.
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Looney put up 6.3 points and 5.2 rebounds while playing just 18.5 minutes per game for the star-studded Warriors. He made the most of his limited playing time, ranking ninth at the position in Real Plus-Minus.
He'd represent the higher-upside option if Boston can coerce him away from Golden State.