Lescott is out of contract at Manchester City at the end of the season, and he seems to be down the pecking order under Manuel Pellegrini - behind the likes of Vincent Kompany, Matija Nastasic and Martin Demichelis.
However, with injuries hitting City hard, Lescott has still featured 13 times and Pellegrini has said that he is not looking to sell in January.
But Besiktas are seemingly confident then can agree a deal for Lescott as they look to spend big in January.
"We are negotiating with Manchester City over defender Joleon Lescott," Besiktas board member Ahmet Kavalci is quoted by Turkish news agency AA.
"There will be some important development about this on Thursday."
Kavalci also confirmed the club are hopeful of finalising a deal for Ronaldinho - who they have been tracking for a number of weeks.
The 33-year-old Atletico Miniero star is being tipped to make an unlikely return to Europe, where he last played with AC Milan in 2010.
Kavalci says sponsorship will help fund what will be a major deal for the Istanbul outfit.
He added: "With Ronaldinho official transfer talks have begun, the cost will be met through sponsors.
"However, in its current state the problem of the transfer is that the cost has yet to be agreed on."
Last week Ronaldinho's brother Roberto de Assis admitted that talks had been ongoing with Besiktas for more than a year.
"They [Besiktas] have been in talks with me for more than year," he told He told Globo Esporte.
"I am here in Europe, but there is no meeting scheduled with anyone."