Sky Sports reports that the Blues are ‘very interested’ in signing the Serbian, 24, who scored 11 goals in 37 Premier League games this season for the Whites, who were relegated.
It is understood that the Cottagers are reluctant to sell Mitrović, but the player is keen to move on this summer.
This is not the first time Everton have been linked with Mitrović, with rumours of a possible move to Goodison Park surfacing in December.
Mitrović first arrived at Craven Cottage on loan from Newcastle United in January 2017, scoring 12 times in 17 Championship games as Fulham earned promotion to the top-flight.
He made the move permanent for a fee which could rise to £27 million in July 2018, but despite being Fulham’s top scorer this term, could not do enough to stave off their immediate return to the second tier.
Everton’s strikers struggled for goals in Marco Silva’s first year in charge; Dominic Calvert-Lewin managed the most with eight in all competitions, while Cenk Tosun scored four and Oumar Niasse did not get on the scoresheet once.
The Blues have also been linked this week with another striker in RB Leipzig’s Jean-Kévin Augustin.
Up front is just one area where Everton are said to be looking to strengthen, with Sky suggesting that they are also searching for reinforcements on the wing, in central midfield, in central defence, at right-back.
A reserve goalkeeper to provide more competition for Jordan Pickford is also apparently on the Toffees’ shopping list.