According to Jon Morosi of MLB Network, the Cardinals have made a formal trade offer and are waiting for a response from Miami.
Stanton was recently named the National League MVP after leading the league with 59 home runs and 132 RBI this season.
Despite his success, the Marlins with their new owners are looking for ways to shed payroll while trading away a player who is set to make $25 million next season, per Barry Jackson and Clark Spencer of the Miami Herald.
Stanton is signed through 2028 with at least $25 million owed per year.
Even if Miami pays some part of the deal, any trade would significantly reduce costs while helping build for the future. On the other side, a contending squad would add one of the top power hitters in baseball.
Although the 28-year-old has sometimes struggled to stay healthy, he has been to four All-Star Games in the last six years and is averaging 44 home runs and 110 RBI per 162 games.