Lescott's contract expires at the end of the season and the England defender appears unlikely to be offered a new deal by manager Manuel Pellegrini, the 31-year-old having been limited to just 10 Premier League starts for City during the 2013-14 campaign.
British counterparts Les Ferdinand, Rob McDonald and Alan Walsh all spent time playing for Besiktas in the late 1980s and early 1990s, and Lescott could become the latest Englishman to sign for the Turkish giants.
"Lescott is still on our transfer wish list," Ozen said, quoted in The Sun.
"Everything will become clear at the end of the season, players will be leaving and arriving but I don't want to disclose too much information yet."
Lescott has made 160 appearances for City since joining the club in a big-money move from Everton in 2009. He has gone on to win the Premier League, FA Cup and League Cup.
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