Boston has the advantage of using part of its $8.4 million disabled player exception gained after the Gordon Hayward injury to sign Monroe, which would give them the ability to pay him more than teams that could only offer the veteran's minimum.
With the loss of DeMarcus Cousins for the season, Monroe, a New Orleans native, could have a chance to play substantial minutes for the Pelicans - an attractive scenario as he heads into free agency.
Monroe, 27, was making $17.8 million in the final year of his contract. He has averaged 11.2 points and 8 rebounds in 23 minutes per 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.