Sky Italia says Lukaku has told Inter he would like them to accept a suitable offer for him from Chelsea.
Chelsea remain determined to re-sign the Belgium striker despite Inter having rejected a second offer of £85m for the 28-year-old, which would have also seen left-back Marcos Alonso move to the Serie A club.
The reigning European champions had already seen a first offer rebuffed by Inter and it is understood neither proposal had made the Italian club change their mind about selling Lukaku.
An offer of between £94m (€110m) and £102m (€120m) could convince Inter chairman Steven Zhang to sell.
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