The Belgium international left Stamford Bridge for Merseyside in 2014, however, Lukaku apparently desires a return.
The Toffees paid a club-record £28m to bring him to Goodison Park, but the 23-year-old wants to push for Champions League football.
Despite Chelsea‘s failures last season, Antonio Conte’s new side will be fighting hard to regain a spot in the top four.
And their £57m move for Lukaku, according to the Mirror, shows Chelsea are keen to add more firepower to their attack.
Lukaku struggled to make an impact in west London during his first spell at the club, but has proved he can succeed in the Premier League.
The striker starred for Everton as he bagged 18 top-flight goals last season, and the Toffees are said to finally accept Lukaku’s intention is to force through a return to Chelsea.
Ronald Koeman’s side value their record signing at £75m and the two clubs are currently in negotiations over a fee.
Should Everton sell they will make a hefty profit on the frontman but face losing an integral figure in their side.
Conte has already brought Michy Batshuayi to Chelsea this summer for £33m from Marseille, but with speculation surrounding Diego Costa’s future, Lukaku is eyed as their latest key target.
It is also claimed one other Premier League side is keen on acquiring Lukaku, but the Belgian has his heart set on unfinished business at Chelsea.
Everton are now expected to heighten their search for a new top striker to lead their attack under new boss Koeman.