The England international has slipped down the pecking order at the Etihad Stadium, with manager Roberto Mancini appearing to favour summer arrival Matija Nastasic alongside captain Vincent Kompany.
This has left the 30-year-old as fourth choice, with Kolo Toure often being selected from the bench.
Lescott is thought to be unhappy at the defensive shift made by his manager and is keen to play first-team football to remain in the hunt for a position in Roy Hodgson’s England plans.
He maintains that he is willing to fight for his place, yet it is unclear as to whether this will be possible.
Everton are thought to be keen to bring back the central defender, whom they sold to City for £22m in 2009, during the winter transfer window.
However, with Toure set to depart for the African Cup of Nations in the New Year, Mancini may be against allowing his back-up man to leave for fear of injury to either of his first choice centre-backs.
The Toffees could still press ahead with a bid, but will be looking to draft in Lescott for a reduced fee.
Meanwhile, striker Mario Balotelli has been urged to return to Italy by national team manager Cesare Prandelli