Doolittle, who is returning from a strained left shoulder injury, pitched a 1-2-3 fourth inning for Class A Advanced Stockton on Friday.
That was his first rehab game, and Doolittle was under the impression Saturday he would pitch again for Stockton on Sunday, but instead he threw a bullpen session on Sunday.
The A's bullpen has struggled most of the season, and Doolittle would be a proven left-hander to help.
Melvin has consistently said he doesn't want to rush Doolittle back, but the two have both said getting him back this season is a realistic possibility. Now it's clear he'll likely be back with the A's relatively soon.
"We'll monitor him, he'll have a few outings there and see how he's doing and then at the right time we'll bring him back," Melvin said.
• Before Sunday's game against the Astros, the A's recognized the family of Sgt. Scott Lunger, a Hayward policeman who was killed in the line of duty on July 22.
Lunger's father, Paul, and his two daughters, Ashton and Sara, threw out the first pitches, and the A's wore Hayward Police hats during batting practice.
"I think it's great," Melvin said of wearing the hats. "I was all for it, I know all of our guys are, too. Any time you can recognize something like this, it means a lot."
• Melvin said designated hitter Billy Butler, who was out of the starting lineup for the second consecutive day on Sunday, will continue to be in the lineup regularly. Butler appeared as a pinch-hitter in the seventh inning of Sunday's 5-4 win over the Astros and grounded out to short.
Butler is mired in a 9-for-56 (.161) slump with no home runs over his last 18 games. Melvin said he wanted Danny Valencia to DH on Saturday, and he wanted Stephen Vogt to DH on Sunday so he could get off his feet but stay in the lineup against right-hander Mike Fiers.
• The A's reinstated right-hander Taylor Thompson from the 60-day disabled list and optioned him to Triple-A Nashville, the club announced Sunday. Thompson has missed the entire season with a strained right shoulder.
• Outfielder Coco Crisp, who left Saturday's game after the second inning due to illness, was back in the lineup on Sunday and went 1-for-5. Melvin said Crisp felt better after Saturday's game.