Renowned publication 'Il Corriere dello Sport' reported on Sunday that the Croatian's time in the Spanish capital is on the verge of coming to an end, despite manager Diego Simeone's comments to the press.
It claims that a deal between the two clubs is already agreed, with Vrsaljko now set to travel to Milan for talks and to undergo a medical on Tuesday.
The World Cup finalists is expected to join Inter on an initial loan deal costing €5.5m, with an obligation to buy the player at the end of the loan for a further €16.5 to take the total fee to €22m.
That money would most likely be immediately reinvested in another right-back, with Santiago Arias and Djibril Sidibe both high on Simeone's wishlist.
The Colombian hinted at a potential move recently as he started following Simeone on Twitter.