West Ham remain favourites to land the 31-year-old central defender after offering a staggering deal that would match his near £90,000-a-week contract until the end of the season and hand him a further three-year deal worth £70,000-a-week on top of that.
The Hammers are desperate to plug their leaky defence with the England international, who is understood to have made up his mind to forego a potential quadruple-winning campaign at City to join a relegation scrap.
Lescott was seen laughing and joking with West Ham's Carlton Cole and Kevin Nolan in Tuesday night's League Cup win at Upton Park after an apparent joke from the Hammers captain about missing out on four medals this season.
But Villa's interest could yet sway him back to the Midlands where he grew up supporting the claret and blues.
Paul Lambert is looking to add experience to his backline and sees Lescott as the best available domestic target, although his wage demands are almost impossible for Villa to match.
They are looking for a loan deal until he end of the season, which City are open to, but it offers less security to Lescott.
Besiktas' bid appears to have fallen by the wayside in the last few days and never really tempted the player who is desperate to catch Roy Hodgson's eye for a World Cup spot.