The Croatia international is currently on-loan at Bayern Munich, having joined in January.
Foot Mercato says United have asked about Perisic during talks over Inter's plans to extend the loan of Alexis Sanchez into the Europa League this season.
Inter want €15m to sell Perisic, though the prospect of a straight swap with Alexis has been raised.
United are not the only English suitor for Perisic, with Everton and Tottenham also keen.
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