St. Louis is looking at catching after star Yadier Molina went out with a thumb injury, and Molina isn't expected back until September, at the earliest.
Batlimore has been using Nick Hundley and Caleb Joseph after losing Matt Wieters for the year with elbow concern. They like the pair defensively, but Suzuki would be an offensive upgrade.
The Twins tried to extend Suzuki, who is hitting .308 and made the All-Star team, but according to Mike Berardino of the St. Paul Pioneer Press, those talks "didn't go very far." Suzuki is a free agent after the year.