The official, speaking on the condition of anonymity because the talks are ongoing, confirmed the request Friday night.
The official also said the teams are discussing compensation if Farrell, who has one year left on his contract, is eventually hired. ESPN first reported the talks.
Farrell was the Red Sox pitching coach for four years before he left for Toronto after 2010. Boston expressed interest in having Farrell take over for Terry Francona after the team's September collapse in 2011, but the Blue Jays would not allow him to leave then.
The Red Sox have also interviewed San Diego Padres special assistant Brad Ausmus, New York Yankees bench coach Tony Pena, Los Angeles Dodgers third base coach Tim Wallach and Baltimore Orioles third base coach DeMarlo Hale to replace Bobby Valentine, who was fired after one dismal season.
General manager Ben Cherington has said he wants a shorter search this year than the one that resulted in Valentine replacing Francona last Dec. 1. That was 64 days after Boston's last game and 62 after Francona was let go.
The Red Sox finished in last place in the AL East this year with a 69-93 record, their worst in nearly 50 years. They were four games behind Farrell's fourth-place Blue Jays, who were 73-89. In Farrell's other season with Toronto, his first as a major league manager, he posted an 81-81 record and another fourth-place finish.
The Red Sox starters had subpar seasons, especially Jon Lester and Josh Beckett, who was traded to the Dodgers on Aug. 25. Beckett was 5-11 with a 5.23 ERA at the time of the trade. Lester finished the season at 9-14 with a 4.82 ERA, both the worst in his seven-year career.
Farrell helped Lester and Clay Buchholz become productive pitchers and is familiar with several Red Sox veterans and minor leaguers.
He also has worked with members of Boston's front office. As Cleveland's director of player development from November 2001 to the end of the 2006 season, he worked with current Boston assistant general manager Mike Hazen, who held scouting and player development positions with the Indians from 2001-05.