Bobby Valentine is expected to meet with Red Sox officials on Monday. He is the only known new candidate.
The Red Sox have already interviewed Sandy Alomar Jr., Gene Lamont and Torey Lovullo for the opening after Terry Francona was not brought back following the club's September collapse.
Valentine, an ESPN analyst, last managed the Chiba Lotte Marines in Japan from 2004-2009. He also managed the Rangers from 1985-1992 and the Mets from 1996-2002, compiling a 1,117-1,072 MLB record and taking the Mets to the 2000 World Series.