The former New York Mets and Texas Rangers skipper will finalize a deal with the Red Sox when he returns Wednesday from a visit to Japan, WCVB-TV, Boston, reported.
A deal was in the works but not yet complete, The Boston Globe reported, while ESPN said Valentine has already accepted the position.
If confirmed, he would be taking his first managerial assignment in nearly 10 years. Valentine managed the Mets for six-plus seasons before being fired in 2002, and also ran the Rangers for eight years, compiling a 1,117-1,072 regular season record in the majors.
His hiring would mark the first major decision by new Red Sox General Manager Ben Cherington, who was awarded the Bosox reins when Theo Epstein left to run the baseball operations of the Chicago Cubs.
Former Manager Terry Francona left the Red Sox in September after winning two World Series titles in eight seasons. His departure was hastened by a late collapse that cost Boston a playoff berth.