Despite Antonio Conte’s side putting forward a bid without any clauses or add-ons, United are holding out for more money.
Ole Gunnar Solskjaer has maintained he is not desperate to sell the Belgian hitman.
And Manchester United will only allow the striker, who cost £75m to prise away from Everton two years ago, to go if Inter match their valuation.
The Serie A giants only have a limited budget to play with but Conte is desperate to sign Lukaku.
Inter have been looking to find a way to make a deal happen, having looked into the prospect of a two-year loan with an obligation to buy.
That did not appeal to United, but even a straight cash bid for the wantaway goalscorer has failed.
Sky Sports say the Red Devils ‘dismissed the Inter bid out of hand’ two days ago.
United are currently away on their pre-season tour and Lukaku has failed to feature in any friendlies yet.
Solskjaer’s men ironically take on Inter today (12.30pm) but Lukaku was ruled out of the contest for fitness reasons.
He is expected to be watching on as Solskjaer’s preferred No.9 Marcus Rashford leads the line in Singapore today, with his future still up in the air.
It remains to be seen if Inter will come back with an improved offer but they know what they have to do.
United are holding out for in excess of £79m, Sky Sports add.
That means Inter fell a massive £26.5m short of United’s valuation, showing there is still plenty of work to be done for the two to potentially reach an agreement.
If the Red Devils do ultimately sell, they will need to bring in a replacement before the Premier League transfer window shuts on August 8.
With three weeks to go until the end of the window, Conte’s Inter are running out of time to persuade United to offload the ex-Chelsea striker.
Yesterday ahead of the United and Inter International Champions Cup clash, Conte said: “I think frustrated is a big word. Lukaku is United’s player and this is the reality.
“You know very well that I like this player, also in the past when I was Chelsea’s coach and tried to bring him to Chelsea. I think today Lukaku is a player with United. This is the reality.
“We will see what happens but for now Lukaku is a United player”
“I think that in this moment if you’re talking about a player from another club it’s right to not talk about Lukaku because we have great respect for United.
“As I said before, I like this player and consider him an important player for us to have a good improvement, but at the same there is a transfer market.
“We know very well which is our situation at the moment and we will see what happens but for now Lukaku is a United player.
“For sure it’s not easy to play without a striker but the market is open so there is still a process for players to come in and out. It’s not easy to play against teams like Juventus and Manchester United without strikers.”