West Ham have reportedly made a move for the 22-year-old Argentine.
The Hammers are said to want the Argentine on loan with an option to buy, with his superior dribbling ability perfect for how Slaven Bilic wants the east London side to play.
The Mirror say West Ham rate the 22-year-old - no doubt previously unheard of to many - very highly.
A helping hand for Zarate?
Should any interest be genuine, Lanzini could be brought to Upton Park with a view to getting the best out of Mauro Zarate.
Zarate, also from Argentina, failed to impress during his first season with West Ham but has been given a second chance ahead of this term.
And the 28-year-old could already be paying the club back after a promising performance against Lusitanos in the Europa League.
Lanzini, then, could further aid the forward, simply as they are countrymen but also both creative, flair players. Dimitri Payet, already signed by West Ham this summer, will also add a creative element to the Hammers.