The 20-year-old has risen to prominence this season during a loan spell with Serie A newbies Hellas Verona.
His razor-sharp displays for the minnows have helped them up to seventh position in their division, and prompted talk of a move once the transfer window re-opens.
Verona themselves are keen to keep their on loan ace, but now Liverpool have upped their interest.
The Reds are believed to have been tracking the winger – who has netted five goals in 22 outings this term – for some time, with scouts from the club lining up targets.
It is thought that contact with the Portuguese outfit was made earlier this week, and that the Merseysiders’ interest is strong.
Iturbe is valued at around £15m, which is a fee Brendan Rodgers can stretch to with his side currently on course for Champions League qualification.
Liverpool are believed to be eager to push through a move quickly in a bid to avoid episodes such as those of Mohamed Salah and Yevhen Konoplyanka in January.