The Celtics will be one of several contending teams with an interest in signing Monroe, league sources said. Boston can use part of its $8.4 million disabled player exception gained after the Gordon Hayward injury to sign Monroe.
Monroe, 27, was making $17.8 million in the final year of his contract. He has averaged 11.2 points and eight rebounds in 23 minutes a game with the Suns. He will be placed on waivers Thursday and will remain there for 48 hours before becoming a free agent if unclaimed.
Phoenix agreed to the buyout after exhausting trade possibilities for Monroe, who arrived with the Suns as part of the Eric Bledsoe deal in November.
Before the trade to Phoenix, Monroe averaged a career-low 6.8 points and five rebounds in limited minutes for the Milwaukee Bucks this season.
For his career, which has included five seasons with the Detroit Pistons, Monroe has averaged 13.9 points and 8.7 rebounds.