The Blues have been locked in negotiations with the Nerazzurri for the Belgian. They recently submitted an £85 million offer plus Marcos Alonso that was rejected.
Inter prefer a straight cash deal for a reported fee of around £102m. It is now reported that the Blues are confident of landing the marksman in the next few days.
The west London giants have been impressive in pre-season, but there has been a similar situation up front with their tendency to squander clear-cut chances.
Lukaku, who bagged 30 goals and 10 assists last term, would provide an ideal solution for manager Thomas Tuchel as the club look to mount a title challenge.
The Belgian was initially happy to stay with Inter next season, but his stance has changed recently after learning about the interest from the Blues.
He believes he has unfinished business at the club. Lukaku was previously with the Blues between 2011 and 2014 but hardly made a mark for them.
The 28-year-old spent two seasons away from the club before he left them permanently for Everton. The Blues attempted to sign him three years later but failed to do so.
Manchester United hijacked the deal at the final hurdle. Lukaku has since joined Inter, where he has played well over the past two seasons.
It looks increasingly likely that they will get their hands on Lukaku this time around with just a £17m difference in the valuation between the clubs.
Stats from Transfermarkt.com