The Italian giants had prepared a bid worth £30million, plus a further £4m in add-ons, but the Belgium international and his representative, Sebastian Ledure, were not able to be contacted on the phone.
Inter were ready to match a Juventus bid made on Wednesday, with an offer much closer to Chelsea’s £40m asking price.
Officials are now concerned that Lukaku is now pushing for a move to Juventus, having previously been told he only wanted to move to San Siro.
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Juventus’s offer was conditional on the sale of Dusan Vlahovic by August 4, who is one of many forwards of interest to Chelsea.
Chelsea have yet to decide whether to move for another striker and simply hoped to sell Lukaku before his return for pre-season training on Monday, in two days’ time.
Inter’s offer was increasingly preferred by Chelsea as they were keen to do a deal right away, with a windfall of around £50m from the sale of goalkeeper Andre Onana to Manchester United coming their way.
Al-Hilal have outbid both Italian clubs by offering £40m, but Lukaku is reluctant to move to Saudi Arabia. All parties are now waiting for Lukaku’s next move to bring clarity after a confusing turn of events.
