Chelsea have seen an £85m ($118m) bid, that included Marcos Alonso heading in the opposite direction, rejected by Inter for striker Romelu Lukaku, Goal can confirm.
Thomas Tuchel is keen to add a world-class forward to his attack as the Blues look to challenge for the Premier League title in the 2021-22 campaign.
Chelsea were hopeful that they could capitalise on Inter's financial difficulties by making a big offer for Lukaku, although the Nerazzurri have thus far proved resistant.
Lukaku said last week that he is gearing up for the new season with the Italian champions after he returned to training, suggesting he wants to stay.
Meanwhile, Inter CEO Giuseppe Marotta has insisted that the forward will not be allowed to leave any time soon, saying: "Lukaku is not for sale. Lukaku is an important piece on the chessboard available to Simone Inzaghi.”
The Stamford Bridge side are in the hunt for a new striker, having seen Olivier Giroud leave this summer.
Chelsea already have Erling Haaland and Harry Kane on their list of targets, but Borussia Dortmund are not willing to sell the former during this transfer window and Tottenham are not letting their star man join their London rivals.
Lukaku, 28, has blossomed into one of the world's top strikers in recent years.
He scored 24 goals and registered 11 assists in Serie A last season as the Nerazzurri secured the league title.
Only Cristiano Ronaldo scored more goals in the Italian top-flight in 2020-21.
Lukaku joined Chelsea from Anderlecht in 2011 but was unable to secure a place in the first team.
He ended up joining West Brom on loan for a year in 2012 and then went to Everton a year later.
Lukaku then joined the Toffees on a permanent deal, leaving Chelsea with just 15 competitive appearances to his name and no goals.
The Blues are already trying to sign Jules Kounde from Sevilla ahead of the new season.
They have been offering several players to the Spanish side in exchange for the defender.
Kurt Zouma, Emerson Palmieri and Kenedy are among the names the Premier League side have floated by Sevilla.
They are trying to get rid of Zouma first to make room in the squad for Kounde, with West Ham also in talks to sign the French centre-back.
Source: Goal.com