Martinez, a first baseman in the majors for 16 years, has been a New York Yankees special assistant and worked as an analyst for the YES Network. Martinez had a career average of .271 with 339 home runs for the Yankees, Mariners, Cardinals and Rays.
The Red Sox also considered hiring Martinez, a source told ESPNBoston.com's Joe McDonald. Martinez had preliminary talks with the team.
The Marlins and the Red Sox were the only teams the Yankees gave permission to talk to Martinez, according to a league source.
Redmond landed his first big league managerial job last week when he was hired to replace Ozzie Guillen. The Marlins this year batted .244, the worst average in franchise history, and scored the fewest runs per game since their first year in 1993.
Eduardo Perez was the Marlins' hitting coach in 2012. Perez will be Houston's bench coach next season.
Information from ESPNBoston.com's Joe McDonald and The Associated Press was used in this report.