The Serie 'A' giants have taken an interest in the Croatian right-back after a series of impressive displays over the past few months, according to Goal.com.
Inter sold Brazil international Maicon to Manchester City in the summer and have struggled to replace him since.
The 20-year-old Vrsaljko is one of the most highly-rated young players in Croatia, having graduated from the Dinamo academy, and blossomed into an important first-team player.
The Croatian champions have a reputation for producing talented youngsters, the latest being teenage sensation Alen Halilovic. Real Madrid star Luka Modric also began his career with Dinamo Zagreb.
Goal.com reports Vrsaljko has previously been a transfer target for a number of European clubs, including Olympique de Marseille, Valencia, Arsenal and Manchester City.
But the Croatian international is under contract with Dinamo until June 2017, and it will likely take an offer of around €8m to bring the Croatian champions to the negotiating table.
Vrsaljko can play left-back as well as right back, and the 20-year-old has four caps for his country, as well as three Croatian First League titles with Dinamo.
Manchester City have several options at fullback, including Alexsander Kolorov, Maicon, Pablo Zabaleta, Gael Clichy and Micah Richards, but could still be tempted if the price is right for one of Europe's brightest young talents.
But Arsenal have a greater need at fullback than the Premier League champions. Injury to Bacary Sagna has exposed a thin back line with Carl Jenkinson filling in for the Frenchman.
On the left-flank, injury prone Kieran Gibbs and Andre Santos battle for a first-team place, but Arsenal manager Arsene Wenger is thought to want more cover.