The Giallorossi were the first top European club to show interest in the talented forward and they seem ready to wrap up the deal for the player.
Il Corriere dello Sport has suggested they have reached an agreement with Hellas Verona to purchase Iturbe for a fee of €16 million.
The youngster may only be on loan with the Gialloblu, but they have the option to turn his loan deal into permanent move and aim to do so before selling him on to Roma.
Meanwhile, the Stadio Olimpico outfit plan to add Iturbe to their ranks as a replacement for Adem Ljajic, who is expected to complete a summer move to Liverpool.
AS Roma are still harbouring Serie A title hopes and they have been made 5/4 favourites to defeat Fiorentina on the road next weekend.