Per The Mirror, both clubs are set to fight it out for the signature of Bournemouth left-back Milos Kerkez.
United are desperate to sign a new left-back after injuries to Luke Shaw and Tyrell Malacia all season.
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Chelsea are also set to pursue defenders if they make sales from their current squad.
Marc Cucurella could depart, while Ben Chilwell has injury issues and Ian Maatsen is likely out the door as well.
Kerkez signed for Bournemouth from AZ Alkmaar in July last year and has impressed since.