The Belgian's agent has issued an update on his future.
Lukaku is said to want out of Everton
Lukaku has repeatedly stressed a desire to leave the Toffees in search of trophies, having scored 25 goals in all competitions last season.
However, the striker's representative, Mino Raiola, told Sportwereld, as quoted by the Mirror, that only "the top clubs" in England can afford him, along with Real Madrid, Barcelona and Paris Saint-Germain.
Lukaku could be using Euro 2016 to generate bids
For the first time in a while, Everton head into the summer transfer window ready to compete with their moneyed rivals, following investment from British-Iranian billionaire Farhad Moshiri earlier this year.
Highly-rated boss Ronald Koeman has already been poached from league rivals Southampton, and Raiola admits Moshiri's ambition could yet keep his client at the club.
"Everton don’t need the money anymore but Romelu wants to play for a club that can win trophies," the Italian said, as quoted by the Mirror.
Lukaku's agent Raiola
“[However] something’s changed at Everton. There’s a new project."
ESPN reported last week that Lukaku has been offered a new contract as a sign of the club's commitment to Koeman.
The Dutchman is said to have been offered a £100 million war-chest with which to turn Everton into Champions League contenders.
And a striker of Lukaku's calibre will be paramount to achieving that.
Is Koeman's appointment a sign of things to come for Everton?