Gordon, 29, is hitting .295 this season with no home runs, 18 RBI and 32 stolen bases. The two-time All-Star played in just 79 games last season after being banned 80 games for violating the Major League Baseball drug policy.
In 2015, Gordon had a league-best .333 batting average and 205 hits. He also stole a league-high 58 times. Gordon tallied 64 steals in 2014, also a league-best. He ended the 2015 season with his first Gold Glove Award and Silver Slugger Award.
Gordon is making $7.8 million this season and has $37.9 million remaining on his contract. His pact includes a $14 million team option in 2021 and a $1 million buyout.
According to the FanRag report, the Marlins are interested in trading Martin Prado, A.J. Ramos and David Phelps.
Last week, sources told USA Today that more than 10 teams inquired about Phelps and three teams had "expressed interest" in Gordon.
The Marlins (41-46) currently sit at third place in the National League East and have won five of their last six games. Gordon is hitting .415 through eight games this month. He hit .313 in June and .371 in May.