The 23-year-old has impressed for Almeria this term, with 10 goals in 19 Primera Liga games.
Now the one-time Real Madrid player could have the chance to switch to the Barclays Premier League.
Speaking after Sunday's 3-2 defeat at Valencia - where Negredo fired home twice, club president Afonso Garcia admitted Almeria's hands are tied if Fulham meet the get-out-clause in the player's contract.
"No one can do anything," Garcia told Marca when asked about Fulham's interest.
With less than 12 hours left before the window closes, Fulham will now be left with only a short period in which to persuade Negredo to make the move to West London.