If all goes according to plan, Bradley will then play a full game Wednesday, and could join the Red Sox as early as Friday when the club begins a three-game series against the Orioles in Baltimore.
Rutledge will stay with Pawtucket to get more at-bats and play the field.
"Both are making very good strides as of late," Red Sox manager John Farrell said.
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.