"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," a United statement said.
"Michael has communicated this to players and staff at Carrington in a busy week for the club."
The 63-year-old German will eventually take charge at United until the end of this season before moving into a two-year consultancy role at the troubled Premier League outfit.
Carrick has been working as United's caretaker boss since Ole Gunnar Solskjaer's sacking.
The former United midfielder, who had served as Solskjaer's assistant, has overseen a 2-0 Champions League win at Villarreal and Sunday's 1-1 draw at Premier League leaders Chelsea.
United host Crystal Palace on Sunday, by which time Rangnick could be in the dugout.
They are then scheduled to play their final Champions League group fixture at home to Swiss club Young Boys on December 8.
That game could be switched to a neutral venue given the new travel restrictions in response to the emergence of the Omicron variant of Covid-19.