Talks between the clubs are at an advanced stage for the 31-year-old to swap Monaco for Turkey.
A transfer fee has been agreed for Chadli, who has only one year left on his deal with the principality club.
However, Chadli has asked for time to consider the offer of a two-year deal from Basaksehir.
Transfer Nexus reported in July that Chadli had his eyes on a move to Antwerp back home in Belgium.
La Dernière Heure confirms that Antwerp, as well as Club Brugge, have had contacts with Chadli.
The finances involved mean the Belgian clubs planned to wait until the end of the transfer window for prices to fall.
Basaksehir are willing to put the necessary money on the table to sign Chadli immediately.
59-time Belgian international Chadli spent last season on loan at Anderlecht, scoring eight goals in 15 league starts.