Southampton and Tottenham Hotspur are also interested in the Juventus midfielder.
The midfielder is expected to leave Juventus this summer, and the Hammers have been linked with a move to bring him to the Olympic Stadium.
Football Italia, citing Tuttosport, claimed last week that Slaven Bilic's side had made an £11.4million bid for the 25-year-old Argentina international.
They are not the only Premier League side interested in his services either, with the same newspaper claiming that Tottenham Hotspur were looking to beat their London rivals to his signature, as reported by Tuttomercatoweb.
However, it appears that both sides will face a fight to secure him this summer, with Zenit St Petersburg and Southampton also keen on the player according to Tuttosport.
According to their report, Zenit’s new coach Mircea Lucescu is keen on the player as he looks to add to his squad for next season.
Unfortunately for them though Juventus want €20million, around £15.6million, for their man, which is a price the Russian side could struggle to match.
Whether Premier League trio Southampton, West Ham and Tottenham are willing to pay that price remains to be seen.