New Inter boss Antonio Conte has made Lukaku, 26, one of his top targets this summer, says Gazzetta dello Sport.
Conte is so desperate to land the Belgian that he has proposed sending Croatia star Perisic, 30, the other way as part of a swap deal.
But Ole Gunnar Solskjaer has apparently already turned down the approach as United hold out on more than £62million for their striker.
However, United would only allow Lukaku to leave should they recoup the £75m they paid Everton two years ago.
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