Inter are understood to have offered an initial €65m (£60m), with an additional €13m (£12m) in achievable bonuses and a percentage sell-on clause for United.
The offer falls some way below United’s original asking price for Lukaku. The Old Trafford club had hoped he would attract bids of up to £85m.
However, Lukaku’s agitation for a move over the past week may mean that United cut their losses and finally allow him to leave for Serie A.
Lukaku failed to report for training in Manchester on Tuesday, instead remaining in Belgium where he was using the facilities at his former club Anderlecht.
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The 26-year-old’s absence followed an incident last week where he leaked training performance data on social media, much to the annoyance of manager Ole Gunnar Solskjaer.
Lukaku’s agent Federico Pastorello arrived in London on Wednesday to discuss Lukaku’s situation with United and push through a move.
United may attempt to replace Lukaku before the close of English football’s transfer window on Thursday, with Juventus striker Mario Mandzukic among those linked.
Solskjaer, however, is understood to be satisfied with the options at his disposal even if Lukaku departs for Italy.
Lukaku’s prospective departure to Inter does not need to be completed by Thursday’s deadline. The transfer window in Italy is open until 18 August.
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