Alomar, who many consider is a lock for the hall of fame, has struggled in a year and a half with the Mets, batting nearly .040 points below his career .302 average.
In 73 games this season, Alomar is batting .262 with 22 RBIs, two homers and six stolen bases. He has walked 29 times while striking out 40 times.
Alomar, the brother of Sox' catcher Sandy Alomar Jr, is expected to start in either Wednesday's three-game series finale against the Twins or Friday's series opener against Tampa Bay. Alomar will likely leadoff, while Willie Harris and Aaron Rowand will platoon in center field and bat second.
The Sox have yet to announce who will be released or demoted to make room for Alomar, but first baseman Paul Konerko, second baseman D'Angelo Jimenez and outfielder Armando Rios are all possibilities.