The Anfield side are keen on signing the highly-rated attacking midfielder after his season-long loan in Serie A finishes in the summer, reports in Italy suggest.
But Liverpool will have to fend off interest from Fiorentina, Napoli, and Juventus for the hot prospect, after impressing so far for high-flying Verona.
The Argentina Under-20 international has previously been likened to fellow native Lionel Messi and is thought to be on the verge of breaking into the Argentina senior squad.
Reds boss Brendan Rodgers would utilise Iturbe as a backup option for striking duo Luis Suarez and Daniel Sturridge, as the youngster's versatility allows him to play across the front line.