The Daily Mail says United have been watching the £70million-rated striker, who has impressed in Italy this season.
The 21-year-old forward has notched 12 goals and provided two assists in 14 appearances so far to emerge as one of Europe's hottest properties.
In total, the Serbia international has scored 41 goals in 98 matches for Fiorentina after making the move from his homeland to Italy three years ago.
Vlahovic's deal at the Italian outfit runs until the summer of 2023 but the club are poised to sell him after he rejected their offer of a contract extension.
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