Corriere dello Sport says United are prepared to sell the Belgium global for €75m.
"It's good that Conte went to Inter, for me he is the best coach in the world", Lukaku said.
The Italian club are now expected to make a formal offer for Lukaku after he heaped praise on Conte - although they face competition from Juventus where current Chelsea boss Maurizio Sarri could join Cristiano Ronaldo in Turin next season and, possibly, Carlo Ancelotti's Napoli.
"He [Conte] knows what I think about him", the former Anderlecht star explained.
Lukaku's agent, Federico Pastorello, has previously stated that his client wants his future sorted out by the end of the 2018-19 campaign and here we are.
Lukaku scored with two close-range finishes as Belgium beat Scotland 3-0 at the King Baudouin Stadium on Tuesday to secure a fourth straight win in Euro 2020 qualifying and move clear of the chasing pack in Group I.
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"I am a big fan of Serie A, who knows me is aware that I wanted to play in the Premier League and that I also want to play in Serie A".
"But I can't reveal it because I have a contract with United and because I respect the club".
"I am going to enjoy my holidays with my family now".
That indicates that the injury is not severe, so quite likely a "Grade I" hamstring injury at the most, which typically takes three weeks to return from.
Those stats don't tell the whole story and the fact that Marcus Rashford is now starting ahead of him at United shows Lukaku that his future lies away from Old Trafford. 'I lost my place and haven't played much.
The other factor in this is that he remains one of the only players United have who they can cash in to get serious money to spend on other areas of the squad where they need to rebuild.