Indians bench coach Sandy Alomar Jr. will interview for the post at Fenway Park on Wednesday.
Torey Lovullo, who managed Boston's Triple-A Pawtucket affiliate in 2010 and was the first-base coach for the Blue Jays this past season, will interview on Friday.
Tigers third-base coach Gene Lamont, who filled that same role for the Red Sox in 2001, will get his chance to speak with Cherington about the job on Saturday.
Thus far, the Sox have interviewed two candidates -- Phillies bench coach Pete Mackanin and Brewers hitting coach Dale Sveum.
One candidate -- Rangers pitching coach Mike Maddux -- withdrew his name from consideration before interviewing.
While Mackanin and Sveum both have managerial experience on an interim basis, Lamont will be the first candidate who has done it on a permanent basis at the Major League level. Lamont managed for the White Sox from 1992-95, going 258-210. He also managed the Pirates for four years (1997-2000), posting a record of 295-352.
Alomar hasn't managed before, but he has a solid pedigree in the game and was considered a leader throughout his 20-year playing career, which concluded in 2007.
Cherington has said he would like to have his manager in place by Thanksgiving.
While the Red Sox try to line up their next manager, former skipper Terry Francona interviewed for the Cardinals' job in St. Louis on Tuesday.