Carrick was handed a permanent contract at the end of last season, after guiding the club to UEFA Champions League qualification, but he's won just one Premier League game so far in the current campaign.
That comes alongside being dumped out of the EFL Cup and losing away at Atletico Madrid in the Champions League with rumours suggesting he could be sacked before the end of October.
Brighton & Hove Albion boss Fabian Hurzeler has been tipped as a possible replacement, but reports from TALKsport claim former Chelsea boss Antonio Conte's representatives have told club officials he's open to a move to Old Trafford.
Conte led Chelsea to the 2016/17 Premier League tittle, followed by Serie A stints at Inter Milan and current side Napoli, with a league crown won at both clubs - plus a spell at Tottenham.
After leaving Napoli over the summer, Conte is looking for a new challenge, and United would not have to pay a compensation fee as they would be required to do with Hurzeler.