The Blues have yet to increase their second offer to Inter for the Belgium international - which was £85m plus left-back Marcos Alonso.
However, the west London club are growing confidence that they can complete a deal, per Sky Sports.
Inter will sell Lukaku if the reigning European champions offer a deal worth £102m (€120m).
The 28-year-old has told Inter that he would like to leave the San Siro if an appropriate offer arrives,
Manchester City had also registered their interest in the Belgium forward.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!