The Premier League duo are reportedly keen on a move for the Argentine winger but face competition for his signature.
The Argentine winger looks set to leave the Italians this summer, with the Premier League duo both reportedly interested in securing his signature according to La Gazzetta dello Sport.
In that report, it was claimed that the Toffees were leading the race to sign the 22-year-old, with manager Roberto Martinez’s side allegedly willing to pay as much as £13.2 million to get their man.
However, it now appears they will face competition from Benfica according to Il Messaggero, with the player thought to be tempted by the idea of a return to Portugal, having had a spell at Porto before his move to Italy with Verona and Roma.
West Ham in more need of a winger than Everton
Having said that, Iturbe's time with Porto was hardly a happy one given he made just six appearances for them in a three year spell, having spent the majority of his time at the club out on loan.
He may then fancy a shot at a chance in England, and both Everton and West Ham would be a good option for him.
At just 22-years-old, he still has plenty to offer and could develop into a top player, and he would get plenty of first team football at both clubs. Out of the two, West Ham are arguably in more need of him than the Toffees, with them seriously lacking in wide players in their current squad.
Whether though, they would stump up the cash reportedly needed to secure him though after such a busy summer already, remains to be seen.