Lanzini has scored one goal in his four caps for Argentina and worked his way into Sampaoli's starting XI in World Cup qualifying.
West Ham have been linked with a number of midfielders in the transfer market, including Manchester City veteran Yaya Toure, and Lanzini's injury could intensify the pursuit for signings in this area.More news: Zinedine Zidane's Successor At Real Madrid Revealed?
Argentina have been training in Barcelona, home to forward Lionel Messi, before travelling to Russian Federation.
Argentina have yet to announce a replacement for Lanzini.
Argentina will play their opening fixture against Iceland on June 16.
Lanzini will likely rehab back in London with the West Ham medical staff.More news: Beckham divorce rumours 'embarrassing waste of time' claims spokesperson
They will now have to deal with a new player being drafted in after Lanzini's serious injury.
Many believed that Inter Milan striker Mauro Icardi, who netted 29 goals in Serie A last campaign was a better choice than Lanzini who could only manage five strikes for the Hammers.More news: Justice Department says heart of health law unconstitutional
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