The midfielder's current deal expires at the end of the season, but he wants to extend his stay beyond his current spell which began when he arrived from Tottenham in 2006.
"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," he told Sky Sports News.
"I feel good at the moment, I've just turned 32 so I've got a bit of time yet."
Carrick has been an increasingly influential figure at Old Trafford since he made his debut. He has played 328 times for the champions, and during his time has claimed five titles.
Meanwhile, Carrick insists that United will respond to their disappointing start to the season.
While Wednesday's draw with Shakhtar Donetsk has left the Red Devils in a decent position in the Champions League, their Premier League status leaves a great deal to be desired.
United head to Sunderland on Saturday on the back of their worst start to a domestic campaign since 1989.
They are in the bottom half of the table and should they get beaten at the Stadium of Light, it will be the first time they have lost three successive league games since 2001.
"You have periods, whether it is through seasons or through years when things don't quite go right," he said.
"You just have to face it and find a way to get through it.
"You can't hide and go under. You have to respond. That is what we will do."
Carrick admits it has been difficult for United to diagnose the issues regarding their form.
"Sometimes it is hard to put your finger on things," he said.
"There are probably a number of reasons. If you don't do enough things well in a game, then you lose it.
"I think we just get back to doing the right things, doing what we believe in. If we do that, in time we will be fine."