Morris, who opened the season in a primary setup spot, has been on the disabled list since May 26 with a herniated lumbar disc, which required surgery.
In his first season of arbitration, Morris is making $1.35 million this season. Morris has four-plus years of MLB service time and is arbitration eligible in 2017, but he will be a free agent after the season. Still, Miami could decide to bring him back.
Morris appeared in 24 games and threw 17 2/3 innings this season, but he was bothered since Spring Training with back issues. He never settled into a comfortable groove, posting a 3.06 ERA and a 1.42 WHIP.
When Morris had his surgery, it was believed he could miss the rest of the season. But he worked his way back and pitched in several game-like situations, including a simulated game last Saturday at the club's training complex in Jupiter, Fla.
The Marlins have back-of-the-bullpen depth with right-handers A.J. Ramos, Kyle Barraclough, David Phelps, Fernando Rodney, Nick Wittgren, Brian Ellington and Nefi Ogando.
Manager Don Mattingly said on Tuesday that the organization hopes to bring Morris back.
"Bryan is a guy we like," Mattingly said. "We know that he is capable, and to me, he still could be part of the future."
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.