The 20-year-old has spent the season on loan at Hellas Verona from Porto, and has impressed with five goals and two assists in Italy.
The Argentine winger has been linked with the Premier League trio previously, but now it seems he has caught the attention of Rafael Benitez at Napoli.
Speaking earlier in the week, Napoli director Riccardo Brigon admitted he hoped a deal could be agreed, but faces a battle with long term admirers, Liverpool, Chelsea and Arsenal, while Hellas also have an option to purchase at the end of the loan spell.
“When it comes to Iturbe we just need to talk with Verona, as they have the option to buy him,” Brigon said.
“I don’t hide that we are interested in him.”
Despite being just 20-years-of-age, Iturbe is currently plying his trade in the fourth different country of his career.
He now finds himself in Italy after beginning his career in Paraguay.
He was signed by Porto, who then loaned him after a handful of games to Argentine side River Plate.