The Marlins are in the thick of the National League Wild Card race, and if Stanton can contribute in any capacity, it would be a bonus.
After an MRI revealed the Grade 3 strain, the Marlins said his best case for a recovery was six weeks, which would mean he could return for the final week of the regular season.
Stanton, who has 25 home runs and 70 RBIs, injured his groin on Aug. 13 against the White Sox while trying to stretch a single into a double on the final play of the game. He went on the disabled list the next day.
With the Marlins on the road, Stanton has been in Miami doing his rehab, but he has yet to get back on the field to do any baseball-related activities.
"His rehab, to this point, has been great," Hill said. "All of the feedback we've been getting has been very positive, and he's in good spirits."
Stanton has had a down season by his standards, batting .244/.329/.496. But in his last 30 games, he hit .274/.339/.513 with six home runs and 23 RBIs.
With Stanton out, the Marlins have mostly been going with Ichiro Suzuki in right field. When Ichiro is off, Marcell Ozuna has been moved from center to right, with Christian Yelich going from left to center.
While Stanton is optimistic about playing late in the year, his status remains unclear until he is on the field testing his legs.
"I don't think we'll be able to truly assess where he's at until he is doing functional, on-field stuff," Hill said. "In terms of the healing process and regaining strength and everything in that area, he's been great."
Joe Frisaro has covered the Marlins for MLB.com since 2002. 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.