The Red Devils secured a battling 3-2 UEFA Champions League victory over AS Roma in midweek, which eased some of the pressure on Carrick, and ended their winless run at nine games across all competitions.
However, Carrick's place at the club is far from secure, ahead of a final game before the FIFA break at home to Aston Villa on November 8th.
Eddie Howe and Julian Nagelsmann are the rumoured frontrunners to replace Carrick, if the former midfielder moves on, but reports from French outlet Foot Mercato claim ex-France boss Didier Deschamps has also been contacted as an option.
Deschamps has been out of work since leaving Les Bleus following their 2026 FIFA World Cup campaign and he's now on the hunt for a new challenge.
Links to the Juventus job have not developed, and he was linked with Real Madrid, prior to their summer reunion with Jose Mourinho.
Deschamps has been informed of United's interest, but nothing formal has been brokered at this stage.