Reports from several media outlets claim that the Red Devils' hierarchy is keen to let Carrick try to turn the side's fortunes around, despite overseeing their worst-ever start to a Premier League season.
United have just one league win so far and sit a point above the relegation zone. Many had expected the manager to be sacked following a terrible week that saw heavy losses to Como (4-1) and Bournemouth (3-0).
There also appears to be unrest in the dressing room, with defender Lisandro Martinez publicly criticising members of the board and captain Bruno Fernandes questioning the team's tactics.
The latter was left on the bench for United's clash with Bournemouth, and stayed there for the entire game with no minutes played.
Supporters made their feelings on the situation clear after defeat to the Cherries, chanting Carrick's name as he left the field before immediately switching to heavy boos as the players departed.
United's next game is against Chelsea on Saturday, October 31st, and reports have stated that Carrick will still be in charge for that match.