The Nigeria international's future at Stamford Bridge looks bleak, having so far failed to feature under Antonio Conte and yet to open talks over a new contract.
Mikel, the Blues' second-longest serving player behind skipper John Terry is out of contract next summer after more than a decade in West London and is therefore free to choose his next club at will.
The Sun claims that United boss Mourinho, who managed the 29-year-old across two separate spells as Chelsea boss, could cash in by making a cut-price bid for the experienced star in the January transfer window.
It is suggested that Mourinho sees Mikel as the right type of player to sit deep and get the best out of world-record purchase Paul Pogba, potentially setting up a reunion at the Theatre of Dreams if terms can be agreed.
Mikel, who controversially joined Chelsea in 2006 despite a £4m agreement being reached with United, revealed last week that he will wait until the New Year before evaluating his next career move.