The Red Devils ended a nine-game winless with a bold 3-2 UEFA Champions League home victory against AS Roma to ease some of the pressure on Carrick's shoulders.
However, his overall struggles so far this season mean the club are expected to consider his position during the incoming November international break.
Eddie Howe and Julian Nagelsmann are the rumoured front runners to come in, if Carrick leaves Old Trafford, but a bold name was considered before Carrick's initial interim appointment midway through last season.
Former manager Erik ten Hag was on the brink of losing his job several times, before the club removed him, and reports from The Athletic claim director of football Jason Wilcox wanted Russell Martin in Manchester.
That option is not expected to be revisited, with Martin's stock dropping significantly, on the back of poor spells at Southampton, Rangers and Leicester City.