The man closest to returning could be Darnell McDonald, who is eligible to be activated on Sunday. McDonald has a right oblique strain.
According to manager Bobby Valentine, McDonald was expected to take dry swings in the batting cage before Wednesday's game.
Ryan Sweeney, who is on the seven-day disabled list as he recovers from a concussion, is eligible to return for Monday afternoon's game against the Tigers.
However, Sweeney hasn't been cleared to do anything yet.
"Sweeney has no activity," Valentine said. "[We need to] allow [his] symptoms to subside."
General manager Ben Cherington said earlier this week that Jacoby Ellsbury (subluxed right shoulder) could return by the first week in July at the earliest.
Left fielder Carl Crawford, who has a sprained ulnar collateral ligament, might be able to ramp up his activities soon, but he probably won't return until some point in July either.
Crawford could start swinging the bat when the Red Sox return to Fenway this weekend. There's no word yet on when he'll be permitted to throw.
As for closer Andrew Bailey, who is recovering from right thumb surgery, has started throwing from a distance of 60 feet at the club's facility in Fort Myers, Fla.