Lukaku is now in Australia on United's pre-season tour, but Ausilio has made a decision to confirm a meeting between officials of his club and the Old Trafford giants over the transfer of the Belgian striker have taken place.
Two years after his big-money move from Everton, there are questions about the 26-year-old's Old Trafford happiness and Antonio Conte's Inter Milan are eyeing a summer move.
Manchester United newcomers gave an excellent account of themselves in their first real test for the club - successfully completing the karaoke initiation in front of their teammates.
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Inter have been keen on proposing a two-year loan deal with a mandatory purchase option for a deal that would have been around €60m to €65m.
"Since then, they're trying to help the players, trying to improve in the way they want us to play and it's all fine so far".
What's more is that he is backed up by the likes of Anthony Martial, Alexis Sanchez and Mason Greenwood - so even if Lukaku does end up leaving this summer, United would still have more than enough depth at centre-forward going into next season.
A move to Inter would see Lukaku belatedly link up with former Conte, who tried to sign him during his time as Chelsea manager. The Belgian scored 27 goals in his first season at the club but managed only 15 in 2018-19.