The former Leeds United right-back has struggled for minutes in a West Ham shirt - and that would not be aided by the club signing Man City's veteran.
Kouyate was deployed in an unfamiliar role by West Ham United boss Slaven Bilic and couldn't prevent a 2-1 defeat to Chelsea.
The West Ham United defender continues to struggle in the top flight.
West Ham United have been linked with the soon-to-be free agent.
West Ham United supporters had more than enough to talk about following their heavy defeat to Manchester City.
West Ham United beat Middlesbrough 3-1 at the Riverside Stadium.
West Ham United's David Sullivan has commented on the deal to sign Jose Fonte.
Hammers supporters have been clamouring for the club to sign a new right-back this month.
Sam Byram joined West Ham United from Leeds United in January 2016.
Sam Byram impressed for West Ham United against Crystal Palace on Saturday afternoon.