Marmol was placed on the 15-day disabled list May 12.
Manager Dale Sveum says Marmol is progressing but is still at least 10 days to two weeks away.
"He's getting his treatment every day, and we'll see what happens," Sveum said.
Sveum said Marmol will likely go to Triple-A Iowa before he returns
"We'll send him down for an inning or two to make sure he's game-ready," Sveum said.
Rafael Dolis has taken over the closer role in Marmol's absence. He picked up his fourth save with a perfect ninth inning on Monday in a 6-4 win in St. Louis.