The former England midfielder will lead training this week but is not being considered to take charge in the interim.
United will outsource for a temporary boss and embark on a thorough recruitment process to find a replacement for Mourinho, who was dismissed on Tuesday after two-and-a-half years in charge.
Carrick was installed as Mourinho's No.2 in the summer after 12 years as a player at Old Trafford.
But despite his senior role United will look elsewhere in the short term.
A figure with close links to the club is thought to be a priority, but head of coaching at United's youth academy Nicky Butt, Wales boss Ryan Giggs and England women's manager Phil Neville are not among the candidates.
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