Matheny is the third person to be interviewed since Tony La Russa retired following the team's World Series championship.
All three candidates thus far have ties to the organization. White Sox third base coach Joe McEwing played for the Cardinals, and Chris Maloney has managed their Triple-A Memphis affiliate the last five years.
Matheny told the St. Louis Post-Dispatch that it was "a great honor" to interview for the job.
"I believe we had positive discussions, and I was able to answer all of their questions," he said, according to the Post-Dispatch. "It's really going to be up to them to sort through all the things they're looking for in that position and who fits it best."
Former Boston Red Sox manager Terry Francona, who was reportedly set to interview with the Cardinals on Friday, has not met with the club, according to media reports.
No more interviews were planned until Tuesday, according to media reports. The Cardinals hope to find a successor to La Russa in the next few weeks.
The 40-year-old Matheny, who played for St. Louis from 2000-04, is a minor league instructor with the Cardinals with no managing experience. He won three Gold Gloves in St. Louis and another with the San Francisco Giants.
Matheny told the Post-Dispatch his lack of managerial experience was "the elephant that walked in with me" to the interview. But that proved not to be a major point of contention, he said.
"That was defused right away. They made it clear that this is a leadership position and that what they were looking for to fill the role is a leader," Matheny said, according to the Post-Dispatch. "Yes, there are the baseball things and the knowledge of baseball, but we talked a lot about the characteristics that are necessary to be a leader at this level and a leader of that clubhouse."
Information from The Associated Press was used in this report.