Ortiz did some baserunning on the field before Wednesday's game and took batting practice indoors.
The Red Sox are 9-12 in the 21 games Ortiz has missed. There's a chance the DH could return at some point during the four-game series in Cleveland that starts Thursday.
"Probably, yeah, if everything goes well," Ortiz said. "I don't have a time set, but I'm getting closer."
With lefty Matt Harrison pitching for the Rangers on Wednesday, Ryan Lavarnway was Boston's designated hitter. The DH has been a revolving spot since Ortiz went down.