Manchester United have already begun the process of identifying possible replacements for the managerial position, according to BBC Sport.
The Red Devils have had a dismal start to the campaign and have picked up just two wins.
They are currently on a seven-match winless streak in all competitions and recently suffered a heavy 4-1 Champions League defeat to Como on the road.
Despite the loss, Carrick will remain in the job against Bournemouth in the Premier League on Sunday, but his long-term future at the club may be uncertain.
BBC Sport claim the club have already begun identifying possible replacements.
Furthermore, Eddie Howe, Antonio Conte and Julian Nagelsmann are understood to have their eyes on the United job as the pressure mounts on Carrick.
Carrick faces a make-or-break game against Bournemouth
The 45-year-old had a splendid spell as interim manager earlier this year. He took charge in January and helped United finish an impressive third in the league standings.
However, the current campaign has not panned out as planned. There was anticipation that the club could challenge at the top, but things have gone pear-shaped.
United have just seven points from as many league matches, and they are struggling in Europe too after disappointing away losses to Atletico and Como.
Hence, the pressure is right on Carrick. The upcoming league game against Bournemouth at Old Trafford could be a make-or-break for the English tactician, in our view.
The Cherries sit below United in the league with just six points and have a day less to prepare, having hosted AC Milan in the Europa League on Thursday (3-0 victory).
Hence, United have home advantage and extra preparation for Sunday. Anything less than a victory could potentially see United part ways with Carrick and find a replacement before the Chelsea trip.
Stats from Transfermarkt.com