Our former midfielder has overseen the 2-0 win at Villarreal and 1-1 draw with Chelsea since Ole Gunnar Solskjaer's departure.
Ralf Rangnick was announced as interim manager on Monday but, while the club follows the regulatory process around a work visa, Carrick will continue at the helm.
Michael has communicated this to players and staff at Carrington in a busy week for the club. Preparation is continuing for the visit of the in-form Gunners,
Following the clash with Arsenal (20:15 GMT), United welcome another London team to Old Trafford on Sunday in the shape of Crystal Palace.