The 31-year-old, who has made 13 appearances for Manuel Pellegrini's side this season, has been targeted for a move in January by the Turkish club
The 31-year-old, who joined City in a £22 million deal from Everton in August 2009, has made 13 appearances in all competitions under Manuel Pellegrini this season.
Lescott is competing for a place in central defence with Vincent Kompany, Matija Nastasic and Martin Demichelis and is now a target for Besiktas, who currently sit fifth in the Turkish Superlig.
The former Everton defender has £2m left on his current contract and Goal understands City are happy to loan him out to a club who will pay 50 per cent of his £90,000-a-week wages.
At present Besiktas are the only club to offer City a nominal transfer fee and the player a full contract and significant signing-on fee.
“We are negotiating with Manchester City over defender Joleon Lescott,” Besiktas board member Ahmet Kavalcı told AA.
“There will be some important development about this on Thursday.”
On Monday, Manuel Pellegrini ruled out the possibility of any players leaving City in the January transfer window.
"I think all the players in the squad at the moment, it is because we need the,” said the Chilean.
“I need all the players."