Clichy was released by City when his contract expired following the 2016-17 campaign, ending a six-year stay at the Etihad Stadium, during which time he won both the Premier League and EFL Cup on two occasions.
Basaksehir announced via their Twitter page that Clichy will undergo a medical and sign his contract on Friday.
Details of the deal have not been disclosed, but reports in Turkey suggest the 31-year-old will pen a three-year deal worth €3million per season.
Clichy joins another ex-City and Arsenal man, Emmanuel Adebayor, in the Basaksehir squad, while former Turkey and Inter midfielder Emre Belozoglu is the club captain.
Playing under coach Abdullah Mucib Avci, Basaksehir secured a surprise second-place finish in the Super Lig last season to seal a spot in the third qualifying round for the Champions League.