Although Atletico's first-choice right-back Juanfran has suffered recent hamstring problem, Vrsaljko, 25, has still struggled to force himself into Diego Siemone's first-team plans this season, making just four La Liga appearances.
The Croatia international has in fact been limited to just 20 appearances in the league for the club since signing a five-year deal in the Spanish capital in 2016 following his arrival from Sassuolo. A winter move is now seemingly on the cards with the full-back said to have asked to leave Atletico when the transfer window opens in January, with his former club interested in bringing him back.
Corrie dello Sport reported that both Monaco and Liverpool have made contact with Atletico's director of football Andrea Berta over whether they can strike a deal for the player in the New Year, reportedly valued at £22m by his current club.
But the same publication now suggests Vrsaljko "has said yes" to an offer from Napoli, who find themselves in desperate need of cover at right-back following Faouzi Ghoulam's cruciate ligament injury.
While Liverpool will be bracing themselves for another offer from Barcelona for Phillippe Coutinho in January, manager Jurgen Klopp has been told he will have money to spend during the mid-season window.
Peter Moore, appointed CEO at Anfield in June, suggests the club will not be drawn into overspending on players, but feels they will be competitive when it comes to battling their rivals for talent.
"From the perspective of competing, we do things the Liverpool way. The chemistry that we build on the field – it's not about buying the most expensive player," Moore said.
"We haven't been shy, obviously the Mohamed Salah purchase for many people has been the top acquisition of the season. We already have Naby Keita coming and I think Alex Oxlade-Chamberlain is doing a tremendous job.
"The investments are being made. It's hard to knock what you are seeing on the field right now.
"What I will say, because I know you are leading up to the question about January, the club continues to look at acquisitions that will strengthen the squad."