The retired Indianapolis Colts head coach confirmed to NFL Network that he met with Vick on Tuesday at Leavenworth (Kan.) Federal Prison.
NFL.com's Steve Wyche also confirmed the meeting through Vick's agent, Joel Segal, who characterized the conversation as "positive."
Dungy told NFL Network that both sides agreed it was best to keep the subject of the conversation with Vick private. Vick, who is completing his 23-month jail sentence on federal dogfighting charges, is expected to serve out his sentence under home confinement in Hampton, Va., from May 21 to July 31.
Vick also is mired in bankruptcy proceedings, having lost much of the wealth he gained from playing football because of his imprisonment. He'll work a $10-an-hour construction job as part of his probation.
After NFL commissioner Roger Goodell makes a ruling on Vick's status with the league, Dungy indicated he would elaborate more publicly about the tenor of his conversation with the quarterback and what role he'll play in the player's future.
Upon his retirement from the Colts following last season, Dungy said he planned to further his work with his foundation and charities and to establish ways to improve the lives of those people who have made bad decisions.
"Where my heart is, is really with our young men right now," Dungy said when he retired. "We have so many guys that didn't grow up like me, didn't have their dad there, and that's something I'm very, very interested in."
Vick pleaded guilty to the dogfighting charges in 2007.
The Associated Press contributed to this report.