Francona confirmed to the St. Louis Post-Dispatch he talked with DeWitt in the owner's hometown of Cincinnati.
"We just had a dialogue," Francona told the newspaper. "I enjoy talking about baseball -- a lot. Without going into details, we discussed pretty basic philosophy. I'd call it an enjoyable, casual conversation."
Multiple sources reported Francona was being interviewed for the Cards' managerial job during the meeting, which came open after Tony La Russa retired following the team's World Series victory over Texas last month.
Francona, who was released by the Red Sox at the end of the season, is also rumored to be under consideration for the Chicago Cubs' managerial opening. The Cubs recently hired former Red Sox General Manager Theo Epstein as the team's chief of baseball operations.
The Cardinals have so far interviewed roving coach Mike Matheny and minor league managers Chris Maloney and Joe McEwing for the job, the Post-Dispatch said.