Carrick's contract at Old Trafford expires at the end of the season, but the England international has admitted that he is targeting a prolonged stay with the Premier League champions.
The 32-year-old told Sky Sports News: "I'd love to carry on playing as long as possible at this club. It's a fantastic club, I've had great times here.
"I feel good at the moment. I've just turned 32 so I've got a bit of time yet."
Carrick has won five league titles and one Champions League trophy during his seven-year spell at the club.