His 13 goals for them come on the back of 17 for West Brom last season, with his form making observers question why Chelsea have not given him a first-team chance.
It remains to be seen whether he will get one next season too, and agent Christophe Henrotay says he has been speaking to other clubs - of which Tottenham are one - about the 20-year-old.
He told Belgian newspaper Het Nieuwsblad: "I'm looking for a club for Romelu. And yes, I've talked to [Tottenham chairman] Daniel Levy once, but that doesn't mean Romelu will definitely join Spurs. That's not a talking point at this moment."
He added that not every club will be able to afford Lukaku should Chelsea decide to sell him.
"There aren't 20 teams that can afford to buy Romelu," he said.
"He won't go from Everton to, let's say, Swansea. There's also a difference between Everton that plays against relegation and an Everton that fights for European football."
Chelsea's decision to loan Lukaku out for a second season has become an increasingly difficult one to understand, with Blues boss Jose Mourinho constantly bemoaning his poor options up front.
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