The Marlins say they will reinstate Morse from the disabled list before Sunday's game against the Chicago Cubs. They optioned Cosart to Triple-A New Orleans after a rough start Saturday.
Morse was placed on the 15-day DL on May 26 because of a sprained right ring finger and he tweaked his back during rehabilitation. He is batting .211 with two homers in 37 games.
Cosart lasted just 1 2-3 innings Saturday, giving up seven runs in a 7-2 loss in his first start after taking a month off to recover from vertigo.