Carrick is under enormous pressure at Old Trafford just months after taking them back to the Champions League as interim.
United currently sit in 13th with just one win from their opening six Premier League games, their worst start to a league season in 40 years.
According to Italian publication Tuttomercatoweb, United are closing in on agreement to bring former Chelsea and Tottenham boss Conte to the club.
Conte has been out of a job since parting ways with Napoli at the end of last season having won the Scuddeto with them in 2024-25.
In a recent interview with The Athletic, Conte revealed he’s looking to return to the dugout sooner rather than later.
"If you go to a club where the history speaks for itself - a history made up of trophies, league titles and victories - you can only honour that history in one way: by having the ambition to bring that club back, if it isn’t there today, to fight for those goals,” he said.
"I know full well that only one team can win every year, but I must carry in my heart, and instil in the hearts of the fans, my players and my directors.
“That spark, that hope that makes you say, ‘F**k, we can win’.
"There are many clubs that have somewhat lost sight of their history. I’d like to go to one of these clubs to dust off that history and make it shine once more.
“Clubs where there’s pressure, where, ultimately, you know full well that you’re not going there just to take part, but to compete."