A deal has been agreed in principal with the United midfielder, and the report claims he will sign the £80,000-a-week contract this summer.
Carrick's current United contract expires in June 2014, but Sir Alex Ferguson is eager to retain his services past that date. The 31-year-old has been in excellent form for the Red Devils this season, and is set to be rewarded with the new offer.
The deal will reportedly include the option of a further year extension after 2016, taking Carrick into his mid-30s with the club.
An Old Trafford source told Goal.com: "It's more or less agreed in principal, the talks have been very easy because the player is very keen to stay at United.
"There has been some interest from other clubs but nobody is anticipating any problems and he will sign a new deal in the summer."
Ferguson recently revealed how delighted he is with Carrick's performances this season, going as far as to say that it's been "his best-ever season at the club".
The England international has one goal and five assists to his name from 29 matches this campaign, and has managed to stay largely injury-free, although he was forced out of Roy Hodgson's most recent squad for the Wembley friendly against Brazil with a hip injury.
The 31-year-old signed for United back in 2006 in a £18.6m from Tottenham. Since then he's helped the club to four Premier League titles, one Champions League and one Club World Cup trophy in six hugely successful seasons at Old Trafford.