The newspaper understands that the club is considering sacking Carrick, just five months after he was given the coaching job on a permanent basis.
The Telegraph also reports that Carrick is close to leaving.
Man United have won just two of their 12 competitive games this season, against Ipswich in the league and Sabah of Azerbaijan in the Champions League.
In the Premier League, the team are 16th with just seven points. It is United's worst league start in 40 years.
Carrick replaced Ruben Amorim in January and got the Reds moving. He won 12 of 17 league games as interim manager, but since the summer, most things have gone wrong.
