The Geordie has held talks with United directors about the post, with an announcement to confirm the appointment potentially as early as today.
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Carrick and former teammate Ole Gunnar Solskjaer have been speaking with United management about taking charge to the end of the season.
United want to make an interim appointment for the remainder of the season after Monday's dismissal of Ruben Amorim.
The Guardian says directors are now leaning towards hiring former United midfielder Carrick, who is available after leaving Middlesbrough last season.
With the Manchester derby this Saturday, it's been suggested the board wish to give the new man as much time as possible to prepare for the game.