Ellsbury tweaked his groin in Philadelphia on May 30 while stealing a club-record five bases.
"Still unavailable tonight," Red Sox manager John Farrell said before Wednesday's game vs. Texas. "He went out and did some more ground base activities with running. We've got to get him to the point of being 80 percent or better intensity level before we can consider putting him back in the lineup.
"As we did with Shane [Victorino], we look at that eighth day of the 15 days as kind of a threshold to make a decision roster-wise. Right now, we're still not thinking about putting him on the DL, but if this continues, obviously we've got to get to that point."
Wednesday marked the sixth calendar day since Ellsbury sustained the injury.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. Jason Mastrodonato is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.