Vrsaljko played a crucial role in Croatia's run to the World Cup final, and was a solid part of Atletico's imperious defence during the 2017/18 season.
His market value has increased as a result of his performances for both club and country - and it appears Inter are willing to meet Atletico's asking price.
It's understood that whilst Atleti have no intention of letting their star right back leave, the player himself is keen on the move, thus forcing the Spanish club's hand.
Vrsaljko has played in Italy before - for Sassuolo - and appears to favour a move back to the country where he made his name.
Atletico's reputation for having a fearsome defensive unit is unlikely to be effected by the sale of the Croatian, with plenty of options to take his place including veteran Juanfran. But the sale would signal that the club was unable to hold onto one of their most valuable assets, something that the side from the Spanish capital will want to avoid in future.