Rangnick, 63, is currently manager of sports and development for Lokomotiv Moscow and United remain in talks with the Russian club over an agreement to release him.
Carrick has been placed in temporary charge while United conduct a thorough process to appoint an interim boss following the sacking of Ole Gunnar Solskjaer last week.
More to follow…
The club are planning to make a permanent appointment at the end of the season and Paris Saint-Germain boss Mauricio Pochettino is their first choice, with Ajax head coach Erik ten Hag also in their thinking.
Discussions are ongoing over a deal that would also see Rangnick remain at the club for two years beyond the end of the season in a consultancy role.
As it stands, Michael Carrick is still expected to be in charge for Sunday’s Premier League game at Chelsea, live on Sky Sports.
This is a breaking news story that is being updated and more details will be published shortly. Please refresh this page for the latest updates.
Sky Sports brings you live updates as they happen. Get breaking sports news, analysis, exclusive interviews, replays and highlights.
Sky Sports is your trusted source for breaking sports news headlines and live updates. Watch live coverage of your favourite sports: Football, F1, Boxing, Cricket, Golf, Tennis, Rugby League, Rugby Union, NFL, Darts, Netball and get the latest transfers news, results, scores and more. Visit skysports.com or the Sky Sports App for all the breaking sports news headlines. You can receive push notifications from the Sky Sports app for the latest news from your favourite sports and you can also follow @SkySportsNews on Twitter to get the latest updates.
Man Utd’s upcoming fixtures November 28: Chelsea (a) – Premier League, kick-off 4.30pm, live on Sky Sports
December 2: Arsenal (h) – Premier League, kick-off 8.15pm December 5: Crystal Palace (h) – Premier League, kick-off 2pm
December 11: Norwich (a) – Premier League, kick-off 5.30pm, live on Sky Sports December 8: Young Boys (h) – Champions League, kick-off 8pm