According to Sky Sports Germany, United are looking into signing the 24-year-old for new boss Erik ten Hag.
However, they will face competition for his signature, as Kalajdzic only has a contract until 2023.
He will be available for roughly £17 million, while Bayern, Borussia Dortmund and Paris Saint-Germain all want to sign him as well.
The striker returned from injury in January, and has since scored six goals in 1,200 minutes at a rate of roughly a goal every 200 minutes.
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