Donaldson, 31, is hitting .243 with eight home runs and 20 RBI in 41 games this season for the Blue Jays.
Sources told MLB Network that there have been no formal trade talks with the Blue Jays regarding the three-time All-Star.
Donaldson had a league-leading 123 RBI in 2015. He also led the league with 352 total bases and 122 runs scored. He is a two-time Silver Slugger award winner.
Donaldson signed a two-year, $28.7 million contract last year. He hits free agency in 2019.
St. Louis could use a bat like Donaldson's. This season, the Cardinals rank No. 18 in batting average and are tied for No. 17 with 97 home runs this season.
Donaldson had at least 29 home runs and 98 RBI in each of the last three seasons entering 2017. Despite that consistency, he is currently in a 1-for-26 slump. He went 0-for-3 Tuesday in the Blue Jays' 4-1 win against the New York Yankees. Toronto has lost five of its last six games, landing the squad in fifth place in the American League East. The Cardinals are in third place in the National League Central.
Donaldson hasn't hit a home run since June 11.
Major League Baseball's trade deadline is on July 31. According to numberFire, Donaldson is projected to hit nine more home runs and drive in 28 RBI for the rest of the season.