The striker looks to be heading for the Old Trafford exit after it became clear that boss Ole Gunnar Solskjaer was happy to let him leave.
Marcus Rashford overtook Lukaku as the Norwegian’s primary target man last season, leaving the Belgian benched more often than not.
Inter coach Antonio Conte is a huge fan of the powerful target man and would love to have him at the San Siro.
The Nerazzurri tabled a £54m bid for Lukaku last week but it was instantly rejected by the Red Devils who are playing hardball.
United paid £75m to sign the 26-year-old from Everton two years ago and want to recoup at least that amount this summer.
And according to The Sun, United chiefs have warned Inter to get serious in their valuation of Lukau and bid accordingly.
United want the ex-Chelsea ace sold so they can begin looking for a replacement striker before the Premier League season kicks off.
Meanwhile, Blues hero Gianfranco Zola believes that Lukaku would be the perfect fit for Inter Milan and boss Conte.
“In addition to the purchases already made, I read that Lukaku could also arrive,” Zola told FC Inter News.
“He would certainly be a player of great impact, he has the right characteristics for the game of Conte.
“And he is a striker who, coming from a championship like the English one, could find so many advantages in Italy.
“At the physical and athletic level, the Premier League prepares you really well right now.
“I am sure he can have a big impact in the Italian championship.”
Lukaku has not featured for Manchester United during their pre-season campaign.
He scored 28 goals in the Old Trafford outfit’s last two Premier League campaigns combined.