Per Ken Rosenthal of The Athletic, Martinez has told people he is "fed up with the Red Sox's inflexibility" and would prefer to sign with a different team.
Jon Heyman of FanRag Sports reported Boston's most recent offer to Martinez was for five years, and he noted at least one other team has extended a deal of that length to the 30-year-old.
Rosenthal noted Boston's offer to Martinez is worth $125 million and wrote the club doesn't appear inclined to increase its proposal after "sensing an absence of competition."
ESPN.com's Jerry Crasnick reported in November that Scott Boras, Martinez's agent, was seeking a deal in the $200 million range.
Martinez has been linked to the Red Sox throughout the offseason. He is coming off a career year with the Detroit Tigers and Arizona Diamondbacks, hitting .303/.376/.690 with 45 home runs and 104 RBI.
The Red Sox finished 26th in MLB last season with a .407 slugging percentage and 27th with 168 home runs.