Curbishley and Wilkins had joined Rene Meulensteen's backroom staff in December, but their roles immediately looked under threat after the Dutchman's spell as head coach was ended on Friday.
Felix Magath was swiftly installed as Fulham's new manager and Sky sources understand there is no place for the experienced duo in the new regime at Craven Cottage.
Curbishley had been absent from the game since his reign as West Ham manager ended in 2008, while Wilkins left his role as Chelsea's assistant boss in 2010.
Confusion still remains about the future of Meulensteen, with reports suggesting he is yet to learn whether he is surplus to requirements.
Fulham owner Shahid Khan decided to take action after last week's 3-2 defeat by Liverpool kept the club bottom of the Premier League, four points from safety.