The left-back, who joined the Premier League champions in 2006, is reportedly unsettled at the club following their pursuit of Everton's Leighton Baines in the summer.
United are expected to return for Baines in January, placing Evra's long-term future in doubt, with his contract expiring next summer.
"No, not at all [concerned]. It is a personal thing," he told Telefoot.
"It is not that Manchester United do not want me to sign a new contract. This whole thing is personal.
"Manchester United would like me to finish my career there, but this is something personal."