According to Portuguese newspaper A Bola, carrying reports from Italy, Liverpool representatives have made contact with Iturbe's agent to sound out his interest in moving to Anfield.
The Porto star, currently on loan at Hellas Verona in Serie A, has been linked with Chelsea as well as Liverpool.
But the Reds do not have first option on the 20-year-old. That belongs to Verona, who can sign the Argentine playmaker with a €15m bid.
And the report claims they've already told Porto they want to sign Iturbe at the end of the season, which means Liverpool will have to wait and see whether the player and club can agree terms on a move.
But it seems Brendan Rodgers is keen to make it clear to the youngster that Liverpool are interested in him as well, and could make a move should he decide against a stay in Italy.
Chelsea were also thought to be watching him earlier this season.
The 20-year-old attacking midfielder has played 23 games in the league for Verona this season, scoring five goals and providing two assists for the seventh-placed team.