Carrick, 45, was made permanent manager after impressing during an interim spell last term, when he led Man Utd to a third-place finish in the Premier League.
But the Red Devils, slumped 18th in the table, have just eight points from their opening 10 matches this season. It is the club’s worst start to a league campaign in 40 years.
Sunday's 4-4 draw with Aston Villa at Old Trafford exposed their defensive frailties, although stoppage-time goals by Joshua Zirkzee and Patrick Dorgu rescued a point.
According to The Athletic, Man Utd intend to dismiss Carrick before their trip to Anfield to face Liverpool on 22 November after the international break.
Work is said to be already underway to identify a successor, with Mauricio Pochettino, currently the United States' manager, understood to be highly regarded by the club.
Former Newcastle boss Eddie Howe and ex-Germany head coach Julian Nagelsmann are also expected to feature prominently on Man Utd’s shortlist.
Any final decision on Carrick’s future will require the approval of co-owner Sir Jim Ratcliffe and the Glazer family, the club’s majority owners, it should be noted.