The Sevilla striker is said to be available this summer.
Everton linked Fernando Llorente
Sevilla are willing to let the striker leave southern Spain, according to the report, and he has as a result put a number of Premier League clubs on alert.
Ronald Koeman is said to be keen to add strength to his strike force with Romelu Lukaku rumoured to be on the move this summer, and his supporting lineup in Aroune Kone and Oumar Niasse yet to make their mark at Goodison Park.
Belgium's Romelu Lukaku has been linked with moves away from Everton
Belgian international Lukaku has apparently got a price tag of £65 million, according to the Daily Mail, which is putting potential suitors off making an offer.
Koeman has not given up hope of keeping the former Chelsea striker, and it was reported last month by the ESPN that the club were considering offering Lukaku a new deal.
In the market Ronald Koeman
However, the same outlet now believe Everton are keeping an eye on former Juventus target man Llorente.
The Spaniard, who was one of Europe's most coveted forwards during his eight years at Bilbao, scored eight goals for Sevilla last term as Los Nervionenses retained their Europa League crown for a third straight season.
Sevilla's Coke and Fernando Llorente celebrate with the trophy after winning the UEFA Europa League Final
Llorente has also made 24 appearances for his country, scoring 7 goals, the first of which came against England in a friendly back in February 2009.