Atletico are reluctant to sell but they will listen to offers and AS reports that the first proposal will be from Inter, who want to sign Vrsaljko on a one-year loan deal with a compulsory purchase next summer.
However, after spending a combined €90m on Thomas Lemar and Rodri, Atletico will be hoping to recoup some cash and if they are forced to sell Vrsaljko, they may prefer a permanent move to be completed in this transfer window.
Inter need a replacement for Joao Cancelo, who impressed on loan from Valencia last season but is now set to sign for the Nerazzurri's Serie A rivals Juventus.
If Inter hesitate in their pursuit, Manchester United are lurking to pounce and will happily pay a higher sum than the Italian side to bring Vrsaljko to Old Trafford this summer.
Corriere dello Sport claims that Vrsaljko would prefer a move to Italy, having previously played in Serie A with Genoa and Sassuolo. He may be tempted by United's greater potential though, and Atletico may be tempted by a higher offer.
However, a deal will not be completed until after the World Cup, by which time Vrsaljko's value may have risen considerably. Croatia are already through to the knockout stages and they are one of only two sides to have kept two clean sheets so far.
Vrsaljko was part of La Liga's tightest defence last season. He was sent off after just ten minutes of Atletico's Europa League semi final against Arsenal, but they still went on to win the tie and the trophy.