The Sun says the Cottagers have made a £26million bid for Brazilian striker Jose.
Slavisa Jokanovic wanted Mitrovic on a permanent deal after helping the club get promoted to the Premier League but a deal has yet to be thrashed out.
Fulham will now wait to see if their offer has been accepted before pressing ahead with a deal.
Jose, 26, has emerged as a player to provide firepower following three successful seasons in La Liga.
Jose scored double figures in the Spanish top-flight after getting promoted with Las Palmas, then netted 34 times in two seasons with Sociedad.