"You can't promise anything to anybody about that, but I would say there's a good chance," manager Bob Melvin said. "I'd like to see that. Things can transpire to where sometimes it just doesn't happen, but I think everybody would like to see that happen."
Blevins, who has gone back and forth between Triple-A and Oakland this season, was brought aboard for the team's third game in Cleveland to take the active roster spot of Brian Fuentes, who was placed on the bereavement list.
It is unclear when Fuentes will return to the team.
It marks Blevins' sixth stint of the year with the A's, who are likely inclined to keep him around for the final month as rosters will officially expand on Thursday.
The left-handed reliever has been called up twice already on the club's current 10-game road trip. He joined the club Friday in Boston and allowed one run on four hits, spanning a combined three innings in two appearances against the Red Sox. He was then sent down between games of a doubleheader on Saturday.
"You obviously want to reward a guy that's taken several bullets for the team," Melvin said. "There have been several times where he probably went out for a second inning thinking, 'I'm the length guy, and I'm going out with a move to make tomorrow, and I'm going to be the guy.' He's had to persevere through a tough season."
Blevins provided the A's with two perfect innings on Wednesday night, striking out three.
Fuentes, who has a 1.59 ERA over his past 22 appearances after posting a 5.09 ERA in his first 38, is eligible to be reinstated on Saturday.