From July 1 to 15, a buyout clause in Kean's deal comes into effect set at €52m.
TMW says Al-Qadsiah are ready to trigger the option and also offer the Italy international an incredible raise on his current Viola wages.
Al-Qadsiah will offer Kean a three-year deal worth €15m-a-season. At Fiorentina, Kean is currently earning €2m-a-year.
Also watching developments are AC Milan and Manchester United.
At Milan, Kean would be reunited with his former Juventus coach Max Allegri. While United are seeking a more mobile striker compared to their current options of Rasmus Hojlund and Josh Zirkzee.