The winger left Cheltenham in 2009 after five years at the club, and scored seven times in Vale's successful promotion push from League Two last season.
Defeat in the play-offs saw Cheltenham miss out, and now they are understood to have made a play for 28-year-old Vincent.
Vale were keen to offer Vincent a new deal, but having failed to agree terms he looks set to leave a year after joining the club.
Vincent began his career with Wolves before moving to Cheltenham in 2004, helping the club win promotion to League One via a play-off final victory over Grimsby Town two years later.
He reunited with former Cheltenham boss John Ward at Colchester United in 2009, spending three years with the club before joining Port Vale.