Cosart (1-3) has a 4.08 ERA in 39 2/3 innings this season.
Fellow righty Mat Latos, who has been on the DL since May 23 with left knee inflammation, was scheduled to make his latest rehab start with New Orleans on Monday night.
"They're progressing. We're moving in a good direction with those guys," Marlins manager Dan Jennings said. "They're building up their pitch count, and hopefully we get 'em in to that 90-100 spot and get them ready to go."
Jennings hinted it could be the final rehab start for both Cosart and Latos.
"It very well could be," he said. "It'll be based upon how they throw and if they're crisp and effective. If not, and it's perceived that they need one more [rehab start], then that could be an option as well."
Right-hander Jose Fernandez is expected to make his second rehab start back from Tommy John surgery on Friday night with Class A Advanced Jupiter.
The 22-year-old allowed eight hits and five earned runs while striking out two in three innings on Saturday night. It was his first game action since May 9, 2014. Fernandez threw 54 pitches, 39 for strikes.