The Croatia international, who played 45 minutes of Atleti's 3-0 Europa League final win against Marseille on Wednesday night, has previously been touted with a move to Manchester City and Arsenal.
According to the Daily Mail, United are considering an approach for the 26-year-old as they are desperate to find cover for the ageing Antonio Valencia.
Atletico would offload Vrsaljko if his £30m valuation is met - roughly double what they paid to sign him two years ago - but that is more than the Red Devils are willing to offer.
Vrsaljko has made 27 appearances for Los Rojiblancos in all competitions and can also slot in further up the field.
As well as bringing in a new right-back, United are also rumoured to be in the market for a left-back and holding midfielder.