According to Rob Bradford of WEEI, chief baseball officer Chaim Bloom said the team is still "in touch" with Bradley's agent, Scott Boras.
"Obviously as the winter has gone on we haven't let that prevent us from making other moves when we've seen opportunity to add good players that fit us and that can bolster this roster but we love Jackie and we've stayed in touch with Scott on him throughout the entire winter," he said.
The San Francisco Giants and Houston Astros are reportedly among teams interested in the former All-Star and Gold Glove Award winner, while the New York Mets are "a long shot" since adding Albert Almora and former Red Sox Kevin Pillar in free agency.
Bradley Jr., a homegrown star for the Red Sox after the team drafted him in the first round out of South Carolina in 2011, hit .283/.364/.450 with seven home runs and 22 RBI for Boston in 55 games in 2020.
Boston has done its due diligence in re-tooling its outfield this offseason, sending Andrew Benintendi to the Kansas City Royals almost exactly a year removed from the trade that sent Mookie Betts to the Los Angeles Dodgers.
Franchy Cordero, who joined the Red Sox in the Benintendi deal, Kike Hernandez, Alex Verdugo, Marwin Gonzalez and Hunter Renfroe are all candidates to fill in on the grass for Boston, which went 24-36 in the shortened 2020 season.
If Bradley Jr. doesn't return, that means just J.D. Martinez remains of the outfield that led Boston to the 2018 World Series, though Martinez has spent most of his time in Boston as a designated hitter.