But the Merseysiders will demand at least £80m for the Belgium striker should he decide to leave Goodison Park.
Lukaku’s agent Mino Raiola has confirmed his client is on the verge of agreeing a new deal worth more than £100,000-a-week.
But he also admitted the nine-goal striker would review his options at the end of the season depending on where Everton finish.
“This is a project which is for the long term and it does not mean that you are fighting for trophies within six months”
Everton boss Ronald Koeman
Lukaku is impressed by the ambition shown by new investor Farhad Moshiri, who wants to turn Everton into Premier League title contenders.
But Ronald Koeman’s men are currently only ninth in table, 20 points behind leaders Chelsea and ten behind fifth-placed Tottenham.
Chelsea, Paris St-Germain and Inter Milan are all keeping tabs on Lukaku and could make a move for him should he become available.
Koeman plans to spend next month with Memphis Depay, Morgan Schneiderlin and Alan Dzagoev all targets.
But he has warned Lukaku that it will take time to turn Everton into contenders.
He said: “We know that due to the people we have inside the club that this is a project which is for the long term and it does not mean that you are fighting for trophies within six months of arriving at a new club.
“We need to invest not only in January, but also in the next summer transfer window.
“I believe that the club are aware of this and that I will receive the time. But it is not easy to get time within football these days.”