The Italian international is wanted by a host of top teams.
Calciomercato suggests that United have a serious interest in the 21-year-old winger.
Fiorentina have slapped a £52 million price tag on their young star to ward of suitors.
But Real Madrid are also circling, meaning that a bidding war in the summer is a possibility.
Chiesa has netted five goals and laid off three assists in 22 Serie A appearances this term.