Lukaku has been linked with a move to the Serie A giants in recent weeks, with Inter set to announce Antonio Conte as their new boss.
Lukaku has failed to impress Ole Gunnar Solskjaer since the Norwegian took over as boss in December.
Reports recently suggested the striker had agreed to leave Old Trafford and join Inter Milan should the clubs agree a deal.
And ESPN now claim that United have told Inter that it will take £80million to take the Belgian to Milan.
It was previously reported that Inter offered United £30million plus Ivan Perisic.
Inter will play Champions League football next season and have also expressed their interest in taking the 26-year-old on loan next season with an obligation to buy in 12 months.
Receiving a fee of £80m for Lukaku would result in a £10m loss for United.
The forward arrived at Old Trafford from Everton for an initial £75m in 2017 but that price has risen to around £90m after a series of add-on clauses were met.
Lukaku is under contract until at least 2022 but is behind Marcus Rashford in the Manchester United pecking order.
Lukaku refused to commit his future to Manchester United towards the end of the season.
“Me? I don’t know,” said Lukaku.
“I am not here to entertain rumours. I am still under contract.”
While his agent Federico Pastorello said the Belgium international is keen to sample other leagues.
Pastorello said in April: ”It’s his second season here and he will still have three years on his contract until the end.
“Let’s see. He’s someone who loves to know a different culture, a different football.
“He sees a way to have a career playing in different countries because he would like to win some trophies and prove himself and say to his children: ‘I won there and I won there and I won there,’ and: ‘I was a very good player in all the top championships’ so let’s see.
“The future is really very open but, at the moment, we don’t discuss about that because really the season is in a big moment.”