Lukaku, who scored 25 Premier League goals for the Toffees last season, has been heavily linked with a return to Stamford Bridge.
The Belgium international joined Everton for £28million from Chelsea in 2014, but his goalscoring qualities have since attracted interest from Antonio Conte.
Conte is keen to bolster his ranks as he bids to build a squad capable of coping with the dual demands of a Premier League title defence and Champions League football next season.
Express Sport understands Lukaku has prompted interest from a host of European clubs including Chelsea, Manchester United and Bayern Munich.
But it appears as if Chelsea are in pole position for his signature after Lukaku made it clear he will not be remaining at Goodison Park next season.
The Daily Mirror claim a deal for Lukaku to seal a sensational return to west London is all but done.
It is said the Blues will pay Everton £70million for his services and he will replace Diego Costa.
Costa’s future at Chelsea looks bleak after he revealed last week that Conte texted him to say he is no longer part of his plans.
Speaking after Spain’s 2-2 draw in Colombia, Costa said: “Antonio Conte has told me by message that I will not continue with Chelsea and that’s it.
“My relationship with the coach has been bad this season and it is clear that he does not want me on the team.
“I guess I have had such a bad season that I can’t continue.
“Right now I’m a Chelsea player because I have a contract, but the coach does not want me there. I have to find a new team.”
Costa has since been linked with a return to Atletico Madrid but he will have to wait until at least January to resign for the club after having their transfer ban upheld.
AC Milan have also expressed an interest in the Spain international, but his £185,000-a-week wages are apparently proving to be a sticking point.