Standard Sport had first reported back in April that Lukaku was keen on a return to Stamford Bridge mainly because he felt he still had ‘unfinished business there’.
The Blues have had their £57m bid rejected by Everton, who slapped a huge £75m price on the Everton star.
But Chelsea feel that £60m will be enough to land their man.
It still means that the Blues will have to pay £30m to buy back the Belgium international who they sold to Everton for just £28m only two years ago.
Lukaku was first signed by the West London club for £18m from Anderlecht back in 2011, but he started just one League match in three years.
With first team opportunities hard to come by, he was sent away on season-long loans in 2012 and 2013, before joining Everton on a permanent basis.
The 23-year-old has flourished away from the capital, having scored 45 goals in the last two years, including a fine brace to knock Chelsea out of the FA Cup Quarter Finals in March.
Chelsea have already signed his Internatiional Belgium team-mate Michy Batshuayi for £33.1m from Marseille.
Lukaku’s arrival at Stamford Bridge will not necessarily mean the departure of Diego Costa. As Atletico Madrid has agreed a £28m fee for Sevilla star Kevin Gameiro.