The former midfielder was pictured arriving at the club's Carrington training ground, with his appointment likely to be confirmed later in the day.
Carrick previously had an unbeaten three-game stint as caretaker boss at Old Trafford in 2021.
The 44-year-old, who won 12 major trophies in his 12-year playing career at United, was appointed manager of Middlesbrough in October 2022.
Carrick guided Middlesbrough to the Championship playoffs in his first season in charge but was dismissed in June after the club finished 10th in the second tier.
United had also been in discussions with former player and boss Ole Gunnar Solskjaer about a potential return to the club.
The Red Devils dismissed Ruben Amorim last week after a dismal 14-month stint under the Portuguese coach.
Caretaker boss Darren Fletcher oversaw a 2-2 draw against lowly Burnley in the Premier League and a 2-1 defeat to Brighton in the FA Cup.
United's exit from both domestic cup competitions at the first hurdle, plus a lack of European football, means they will play only 40 matches this season - their lowest number since the 1914/1915 campaign.
The 20-time English champions are seventh in the Premier League, but just three points outside the top four and one point behind fifth-placed Brentford.
A top-four finish would guarantee a return to the lucrative Champions League and top five is likely to be enough thanks to the strong performance of English sides in European competition so far this season.
United host local rivals Manchester City on Saturday in what is likely to be Carrick's first game in charge.
