Drew continues to make progress after suffering a concussion on March 7, when he was hit in the helmet by a pitch.
Drew will play at least three more games for the Sea Dogs and could join the Red Sox on Monday for the home opener.
"I've been out of the game for three and a half weeks now, so I'll try to see as many pitches as I can, get as many at-bats as I can," Drew told reporters in Portland before Thursday's game. "I don't want to say it's Spring Training, but I've got to get my legs under me a little bit and progress with innings, and hopefully head back up there."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. This story was not subject to the approval of Major League Baseball or its clubs.