Reports coming out of Turkey on New Year's Day claimed Besiktas were in discussions to sign England international Lescott during this month's transfer window.
Lescott's future has been the subject of conjecture for some time with the former Everton man's contract due to expire at the end of the season.
The 31-year-old has found himself down the pecking order at City this season with Vincent Kompany, Matija Nastasic and Martin Demichelis all ahead of him in Manuel Pellegrini's plans.
Lescott's representative, James Featherstone of OmniSports Management, has confirmed Besiktas have made contact over the defender, but that Lescott is focused on life at City until he is told otherwise.
"It is true that Besiktas have made contact regards Joleon," 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."