The person spoke on condition of anonymity because no announcement was made. The interview took place in Cincinnati, where Cardinals chairman Bill DeWitt Jr. lives.
Francona managed the Red Sox for eight seasons and left after they wasted a nine-game September lead in the AL wild-card race.
St. Louis is seeking a replacement for Tony La Russa, who retired two days after winning his second World Series in 16 seasons with the Cardinals.
More interviews are planned for Wednesday, believed to be with third base coach Jose Oquendo and Hall of Fame second baseman Ryan Sandberg, who managed the Phillies' Triple-A team last season.
St. Louis previously interviewed Mike Matheny, Joe McEwing and Chris Maloney. Matheny and Maloney have organizational ties and McEwing played for St. Louis.
The 48-year-old Oquendo has been the third base coach the last dozen years. He played his final 10 major league seasons with the Cardinals from 1986-95 when he was nicknamed the "Secret Weapon" as a nod to his versatility.
St. Louis has received permission from the Phillies to talk with Sandberg, ruled out earlier for the managing job with the Cubs, the team he starred for from 1982-97.
After he left the Red Sox, there were reports players drank beer and ate fast food fried chicken in the clubhouse during games rather than root on their teammates. The Boston Globe reported the club was concerned he was "distracted," living in a hotel while separated from his wife and taking painkillers to deal with knee operations. Francona has said his personal life didn't affect his performance.
Boston ended an 86-year championship drought in 2004, Francona's first season, when the Red Sox swept the Cardinals in the World Series. Francona also managed the Red Sox to a sweep of Colorado in the 2007 World Series.
Francona is the second-winningest manager in Red Sox history with a 744-552 record and 8-0 mark in the World Series.
Francona and Cardinals general manager John Mozeliak didn't respond to requests for comment.
Copyright 2011 by The Associated Press
