Lukaku, 22, has scored 18 goals in 29 games for the Toffees this season but with the club languishing in mid-table, the former Chelsea man is understood to be open to leaving this summer in search of European football.
And his agent, Mino Raiola, has hinted a summer move could be on the cards.
He told Belgian outlet DH: “He’ll keep getting stronger.
“Everything depends on his work and on luck. He’s already ready to play in Europe’s best teams.
“I’m not surprised by his performances. He has a heart of gold, which is very important in football, and has a lot of talent.
“Since we’ve been working together we’ve put a structure together that allows him to only think about football.
“This has allowed him to think exclusively about his personal objectives.”