Manager Dan Jennings said Cosart could be pitching in Miami around Sept. 8-9, when the Brewers are at Marlins Park.
"He's going to have another rehab start," Jennings said.
Cosart pitched for the Hammerheads on Thursday, giving up four runs in five-plus innings. The right-hander allowed one run through five innings, but he labored in the sixth.
"They said the first five innings were very good," Jennings said. "He kind of hit the wall there in the sixth inning. We felt somewhere in that 60-pitch mark that might happen."
Cosart threw 70 pitches (57 strikes) and he struck out four while walking one.
Cosart has been on the disabled list at the Major League and Minor League levels this season with vertigo. A few weeks ago he saw a specialist in Chicago, and it was determined he had a left inner ear disorder.
Thursday was his second game action since July 17. Last Saturday, he threw 44 pitches in a Gulf Coast League game.
Cosart is 1-4 with a 5.36 ERA in nine big league games, with eight starts. He was optioned to Triple-A New Orleans after a rough start on July 4 against the Cubs at Wrigley Field. He gave up seven runs in 1 2/3 innings.
"We feel he needs another start down below," Jennings said. "And then somewhere around [Sept. 8-9] he will factor in and get back into the rotation here in the big leagues."
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.