The Serie A side are desperate to land Lukaku this summer following Conte’s appointment.
But Inter have already seen multiple offers rejected by Manchester United.
Lukaku is valued at £80m by the Old Trafford outfit – a fee deemed far too high by Conte’s men due to their lack of significant transfer funds.
The Italian outfit saw a £54m bid rejected over the weekend, and have also failed with multiple loan offers.
Gazzetta dello Sport report that San Siro chairman Steven Zhang has told the board he cannot go any higher than the £54m recently offered – unless players are sold.
And this is what the Inter bigwig will reiterate to Conte on Monday during a team dinner.
Conte publicly admitted he wants Lukaku brought in over the weekend.
And Ivan Perisic and Mauro Icardi are two players who could be sold to free up funds for the striker.
The latter is destined for a move away from the Nerazzurri after falling out of favour with the board and some sections of the fanbase.
Perisic has previously attracted interest from English clubs in the past but appears unlikely to join the Premier League this summer.
Lukaku, meanwhile, is keen to see his Inter move forced through.
The Belgian hasn’t played for United during any of their pre-season games so far.
And he has already talked up Inter and Conte in an interview earlier this summer.
“It’s good to see Conte has joined Inter. For me he is the best manager in the world,” he told reporters while on international duty with Belgium earlier this summer.
“I’ve already taken a decision about the future but I can’t reveal it because I have a contract with Manchester United and because I respect the club.
“I am a big Serie A fan, those close to me know that I have always wanted to play in the English league and in the Italian one, I love Italy.
“And then Cristiano Ronaldo arrived, [Maurizio] Sarri will go to Juventus, [Carlo] Ancelotti is at Napoli, it will be an exciting Serie A.
“The club and my agent will talk about it but I have already made my decision. Conte knows what I think about him.
“You know I’m not somebody who likes to talk about my personal relationship with managers, but I’m a Manchester United player.
“If something happens, you know, I think the teams and my agents have to do the talking.”