The pressure is on the Nerazzurri to raise the funds needed for the transfer because Serie A rivals Juventus are now showing an interest in the striker.
It is understood that United want a cash-only £75m fee from Inter if they are to sell the Belgian international.
Lukaku is staying professional and even reported for United's pre-season training early.
He is under contract until 2022 but it is understood that he wants to move and United would sell at the right price.
Lukaku, who is currently out in Australia with his United team-mates, wants a deal concluded as quickly as possible.
Sky Sports News is home to three new shows dedicated to bringing you the very latest news from this summer's transfer market.
Start your day with Good Morning Transfers at 9am as our team of reporters and pundits bring you the latest news and insight. Transfer Talk then follows at midday, delivering the biggest stories that matter to you. And join us at 7pm for the definitive round-up of the day's news with The Transfer Show.
And as well as tuning into Sky Sports News, don't miss a thing with our dedicated Transfer Centre blog.
There's also the Transfer Talk Podcast, the daily UK, Regional and European Paper Talk, plus features across skysports.com and the Sky Sports app.