The ambitious Goodison Park club have no desire to sell the in-form Belgian who has two years left on his contract but he has made it clear he wants to play for a Champions League club.
Lukaku is now top scorer in the Premier League this season with 23 goals, while he has also assisted a further six.
That allowed Lukaku, who has scored 12 goals in his last 10 appearances, to pull away at the top of the standings.
Chelsea will have to scale Everton's monumental asking price, however.
Lukaku has a £100 million price tag on his head thanks to his current club, but that will not put off Chelsea when the summer transfer window opens.More news: New contender in hunt for alien life discovered by astronomers
Manchester United are eager to sign a long-term successor for Zlatan Ibrahimovic, especially with the Swede's future beyond this season at Old Trafford not certain.
Rumours will reignite after Lukaku admitted that he watches the official channels of some of Europe's top clubs.
The Toffees are determined to keep hold of their prized asset, but will let the wantaway man leave if a world record offer comes in.
"I'm subscribed to everything you can think of: Chelsea TV, Manchester United TV, Real Madrid TV".
The 23-year-old England global became the first Spurs player since Jimmy Greaves in 1969 to hit 20 goals in three successive top-flight seasons after netting in the club's 4-0 win over Bournemouth last weekend. The Merseyside club see Lukaku as the ideal player to build their team around by recruiting heavily in the summer.