One person told Heyman they "didn't see any way" Stanton would agree to go to the Cardinals, while another person said the four-time All-Star would "100 percent" prefer the San Francisco Giants.
MLB Network's Jon Morosi reported the Cardinals had set up a meeting with Stanton's representatives Friday.
The Giants had a similar meeting with Stanton's representatives Thursday, per Craig Mish of SiriusXM.
On Nov. 19, Morosi reported the Cards made a formal trade offer to the Marlins for the 28-year-old.
The Marlins have been shopping Stanton since the end of the 2017 season, with Barry Jackson and Clark Spencer of the Miami Herald reporting the team's new ownership group wants to bring the payroll down to $90 million next season.
Stanton has 10 years and $295 million left on the 13-year contract he signed after the 2014 season. The deal also includes a player opt-out after the 2020 season, per Spotrac.
Stanton is coming off his best MLB season. He hit a career-high 59 home runs to go with 132 RBI, a .631 slugging percentage and 159 games played. He also became the first player in Marlins history to be named MVP.