Aceves, who is being used exclusively as a starter for Pawtucket, is 2-0 with a 1.38 ERA in his first two outings.
"He's going to be evaluated independently based on his ability to execute with the consistency that we outlined when we optioned him to Pawtucket," said manager John Farrell. "While he's in the starting role there, we feel like that's the best place for him to gain that consistency, and yet he wouldn't be the only option if a need were to continue to arise to support the bullpen."
The early reports on Aceves are encouraging, but the Red Sox would like to see a larger body of work before they bring him back.
"He's had two starts, he's gone six innings each time," Farrell said. "Solid performance numbers and yet I think after he got through the first inning plus last night, where he used more of his overall pitch mix, he pitched a little bit better. So again, it's still a matter of gaining that consistency."
Ian Browne is a reporter for MLB.com. Read his blog, Brownie Points, and follow him on Twitter @IanMBrowne. Jason Mastrodonato is a reporter for MLB.com. Follow him on Twitter @jmastrodonato. This story was not subject to the approval of Major League Baseball or its clubs.