Liverpool are said to be after Kerkez, while United have him on a long list of possible left-back additions.
The 21-year-old's contract with Bournemouth runs until the summer of 2028.
Sky Deutschland's Florian Plettenberg is reporting: "Milos Kerkez is drawing interest from several Premier League clubs.
"Liverpool is pursuing him, and he’s also on Manchester United’s long list of options. MUFC are actively searching for a new left-back, but the 21-year-old Hungarian is not currently at the top of their list.
"Contract with Bournemouth valid until 2028."
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