He will start a Minor League rehab assignment at Double-A Portland on Thursday.
Because Drew is on the seven-day disabled list, he is only eligible to play five games on his rehab assignment.
Farrell said the current plan is for Drew to play four games, which would put him on track to play at Fenway Park on Monday.
"Once we were getting down to the last couple of days [of Spring Training], he started to turn the corner in terms of day to day feeling consistent without the spinning sensation that he was going through," said Farrell. "He's in a good place right now, all things considered."
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.