The Croatian defender has long been a target of Arsene Wenger, and the Gunners will be boosted by the news that Serie side Milan are no longer in the hunt for the player.
Vrsaljko - a powerful and promising fullback - appeared for Croatia in this summer's World Cup, boosting his already developing reputation.
The 22-year-old enjoyed an impressive first season in Italy with Genoa, and interest in the player is high.
Along with FA Cup holders Arsenal, Inter Milan and Fiorentina are said to be monitoring his situation.
Milan, however, would appear to be out of the race after their CEO Adriano Galliani said that he would not be joining the seven time European Champions.
Galliani is quoted on talkSPORT.com as saying: "Vrsaljko will not come."
With Bacary Sagna having left for rivals Manchester City, the Gunners are in need of a right-back and Vrsaljko could be a a solid replacement.
Although Wenger's side have been linked with Frenchman Mathieu Debuchy, Vrsaljko would offer the added benefit of still being relatively young.
Arsenal have already sealed a deal for Alexis Sanchez and are expected to complete more signings before the end of the window.
Real Madrid and Germany midfielder Sami Khedira remains the most likely to join the North London side, with rumours intensifying of negotiations reaching an advanced stage. It would appear the only potential hold-up on the deal is the player's wage demands.