Mainoo, 22, seriously struggled for minutes under former manager Ruben Amorim, and even pushed to leave the club on loan last summer.
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Amorim has since been dismissed and Carrick has been appointed as his interim replacement, beating rivals Man City 2-0 in his first game at the helm.
The England international was instantly trusted by Carrick, who played Mainoo for the full 90 minutes in the win over Man City.
According to Fabrizio Romano, Mainoo has now decided to stay with his boyhood club having previously thought about once again pushing for a move away this month.