The 31-year-old is behind the likes of Vincent Kompany, Matija Nastasic and Martin Demichelis in the pecking order at Eastlands.
Lescott's current contract with City is due to expire at the end of the season.
"It is true that Besiktas have made contact regards Joleon," Lescott's representative, James Featherstone, told Sky Sports.
"Joleon is able to talk to interested clubs now as he is in the final six months of his contract and a number of clubs have expressed an interest in him.
"However, at the moment Joleon is focused on doing his best for Manchester City and is ready to give his all when called upon.
"Joleon is a Manchester City player, so if any club are interested in signing him prior to his contract expiring they have to agree something with Manchester City first and then we will see if we can take it any further."