"High number of innings out of the bullpen. We need a fresh arm and someone capable of doing multiple innings," said Red Sox manager John Farrell.
Wright went five innings for Pawtucket on Wednesday.
"He's available for a couple of innings today," said Farrell.
The Red Sox have off-days coming up on Monday and Thursday, and Farrell will soon announce how the rotation will be arranged. Rick Porcello, who has struggled mightily of late, might skip a start or at least be pushed back.
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, follow him on Twitter @IanMBrowne and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.