Despite their reported interest, Morosi added the Cards have yet to engage the Jays in formal trade discussions.
The 31-year-old Donaldson is struggling through a down season; he is batting just .238 with eight home runs and 20 RBI.
He missed considerable time due to a calf injury and has been unable to find his All-Star form.
Donaldson made three consecutive All-Star teams from 2014 through 2016, and he was named American League MVP in 2015 when he hit .297 with 41 home runs and 123 RBI.
Entering the season, Donaldson had clubbed at least 29 homers and driven in at least 98 runs in three straight campaigns. He signed a two-year, $28.7 million contract with the Jays last year, and can become a free agent in 2019.
The Cardinals are playing Jedd Gyorko at third base, and he has been their top-performing hitter. In the event of acquiring Donaldson, however, he could be moved to the middle infield.
The Cardinals—who are 4.5 games behind the Milwaukee Brewers for the NL Central lead—rank 18th in batting average, 19th in runs scored and 20th in home runs this season.