Since the sale of Neymar to Paris Saint-Germain , the La Liga outfit have been linked with several possible replacements, with Liverpool's Philippe Coutinho and Borussia Dortmund's Ousmane Dembele known to be on their shortlist.
However, both clubs remain keen on keeping their star men - with Liverpool said to be ready to rebuff an £138m bid for Coutinho - and according to reports in Argentina, the Catalan giants are prepared to move on.
It has been suggested that a surprise move for Lanzini could be in the offing, with Barcelona allegedly admirers of his ability to play in a number of positions.
Since first linking up with the Hammers in 2015, the 24-year-old has contributed 14 goals in 61 Premier League appearances, while the Argentine still has three years remaining on his existing deal.
West Ham boss Slaven Bilic has previously claimed that Lanzini is happy at the London Stadium.