United gave permission for Lukaku to train with his former club Anderlecht on Monday. However they expected him to report back to their Carrington training base today.
But Lukaku refused to return to Manchester and has instead remained with his former club in Belgium, as he attempts to push through a transfer away from Old Trafford.
Both United and Lukaku’s representatives have so far refused to comment on his situation.
The confusion means that Antonio Conte’s Inter Milan are increasingly bullish of signing 26-year-old Lukaku – who is valued at £75 by United – at a bargain price.
Earlier this summer Inter failed with a bid of £54m, while last week Lukaku verbally agreed to join Serie A champions Juventus in an audacious swap deal for the Argentine forward Paulo Dybala.
However, that deal broke down when Dybala refused to lower his £350k-per-week wage demands.
Inter now sense an opportunity to finally sign a player they have courted all summer, but have so far struggled to raise the necessary funds for.
Last weekend, Conte said he was “very hopeful” of brining Lukaku to the San Siro.
“I understand there are some gaps that need to be filled but at the moment I am very hopeful that this will happen,” he said after his club’s pre-season match against Tottenham Hotspur in London.
“At the same time, I’m working with a great group of players that gives me lots of satisfaction.”
The Italian transfer window does not close until September 1, giving Inter more time to complete a switch for the forward.
They have already spent close to £100m this summer, with Austrian international Valentino Lazaro their most expensive signing, arriving from Hertha Berlin for £20m.
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