The Daily Mail says the former Charlton and West Ham boss is on a short-list at Craven Cottage with Sven Goran Eriksson and Mark Hughes.
However, the cost of bringing either Eriksson or Hughes to Craven Cottage would seem to be prohibitive.
That has opened the door for Curbishley, who has not managed since parting company with West Ham in September 2008.
The 52-year-old is no stranger to working on a tight budget, which is likely to appeal to Fulham owner Mohamed Al Fayed, having excelled on a shoestring with Charlton during 15 largely successful years at The Valley.