The 19-year-old who made 24 appearances in his debut A-League season, as well as three cameo appearances at the recent FIFA World Cup has attracted interest from a number of clubs in Europe.
Arzani is expected to move from Melbourne City to Manchester City and then out on loan in a similar deal to that of Aaron Mooy in 2016.
But according to ESPN, Roma are monitoring the situation and "are ready to offer the forward a pathway to first-team football."
Roma's director of football, Monchi, made his name at Sevilla for discovering young, generally unheralded, talent and then selling them on to Europe's biggest clubs including Sergio Ramos, Dani Alves and Ivan Rakitic.
Arzani's link to Roma possibly comes through his agent, former Socceroo Vince Grella, who also represents Daniel de Silva, who had a contract with the Serie A club in 2014 only for the deal to fall through a year later.