Romelu Lukaku has told Inter Milan 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, according to Sky in Italy.
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.
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An offer of between £94m (€110m) and £102m (€120m) could convince Inter chairman Steven Zhang to sell.
Premier League rivals Manchester City had also registered their interest in signing Lukaku earlier this year, but no offer was made as Inter showed no intention of selling at the time.
Tuchel: Lukaku a fantastic player
Speaking after his side's pre-season friendly against Tottenham on Wednesday evening, Chelsea head coach Thomas Tuchel refused to directly address the transfer situation but described Lukaku as a "fantastic player".
"I will not talk about players who don't play in my squad," Tuchel said. "And Romelu Lukaku is a fantastic player but he's a player from Inter and it's with all the respect I will not talk about him in this situation.
Asked about Lukaku having expressed his desire to return to Stamford Bridge, Tuchel added: "Everybody wants to come (to Chelsea) hopefully. Not everybody unfortunately, but you can imagine that a lot of players want to come and join.
"The board is not offering players. That's not the way it works so far. We're talking with the board about players and if our opinions and the scouts conclude, then we target players who, in all our opinion, could make our squad stronger, which is quite a challenge to find.
"We don't only talk about talent but also attitude because we have a strong squad and there are some players of which we think they could be a good target and good add-ons and good improvement in our squad."
Lukaku played a key role in Inter's Serie A win last season, scoring 24 goals.
Inter need to reduce their wage bill this summer and title-winning boss Antonio Conte left the club in May amid concerns about plans to cut his budget.
Chelsea are determined to sign a world-class striker and their other main target this summer has been Borussia Dortmund's Erling Haaland.
Lukaku previously spent three years at Chelsea after signing from Anderlecht as a teenager in 2011.
However, he made only 15 appearances for the club - failing to score a goal - before moving to Everton for £28m in July 2014.
He was close to a return in July 2017 but opted to join Manchester United for £75m. Inter signed him from United for £73m two years ago.
'CHELSEA HOPE INTER HOLD NERVE OVER LUKAKU'
Sky Sports News' Kaveh Solhekol on The Transfer Show:
"Romelu Lukaku has made it clear to Inter that he would like to move to Chelsea if Chelsea make an acceptable offer for him.
"Chelsea are in talks with Inter, they will increase the second offer they've made worth £85m plus Marcos Alonso.
"Inter have told them they would prefer a cash deal and it has to be between 110 and 120m Euros.
"Chelsea are minded to increase their offer because they want to sign Lukaku in the next few days.
"But this is where it becomes interesting as some people at Inter think this type of deal would be impossible to turn down as they have financial problems and a deal of this size would go a long way to solving them.
"There are others at the club who feel strongly Lukaku should not be sold, so there is a lot of internal politics going on at Inter. And the final decision makers will be the
"Chinese owners and chairman Steven Zhang - is he going to sanction the sale of Lukaku, a player who Inter's fans call the King of Milan and whose goals helped them win the title for the first time in 11 years?
"The fans and Ultras will not be happy if Lukaku is sold on the back of Antonio Conte leaving due to not being supported in the financial market.
"Chelsea, though, will be hoping he holds his nerve and decides they have to take 120m euros for a 28-year-old."
What does Lukaku deal mean for Haaland?
Sky Sports News reporter Dharmesh Sheth:
"It's a very good question as Chelsea were very interested in Haaland. Who knows, they could still be interested. Could you see a situation where they could try to break the bank by bringing in Haaland and Romelu Lukaku? That seems unlikely.
"This could drag on into next summer. Borussia Dortmund have said that there's no gentleman's agreement with Haaland as there was with Jadon Sancho. All of the noises coming out of Germany are saying that Dortmund won't sell both those players in the same transfer window.
"Haaland has a release clause that kicks in next summer. With Man City in for Harry Kane and Chelsea in for Lukaku, where does that leave those two clubs with regards to Haaland? Maybe they both feel they could pair those players with Haaland but next summer there will be more clubs who could afford him."
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