Reed reportedly will be dealt in exchange for three Red Sox prospects. He will be a free agent after the season.
Reed, 28, is 1-2 with a 2.57 ERA and 19 saves in 21 opportunities over 49 innings in 48 appearances this season. He has been the closer for the Mets since Jeurys Familia underwent surgery in May to repair a blood clot in his pitching arm.
Reed would be expected to return to a setup role behind Red Sox right-handed closer Craig Kimbrel.
According to the New York Post, the Mets will get three minor league relievers in the trade -- Jamie Callahan (Triple A), Gerson Bautista (Class A) and Stephen Nogosek (Class A).