Sky Sports are reporting that Argentina have asked Everton to make Ramiro Funes Mori available to play in this summer's Olympics.
The football tournament begins on August 3, just 10 days before the Premier league season begins.
Clubs are not obliged to release their players for the Olympics, however, as the games are not on the FIFA calendar.
Argentina head coach Gerardo Martino wants Funes Mori for both the Olympics and Copa America, which is being held in the United States in June.
He said: "Let's hope we can have him for both competitions. We've already spoken with Roberto Martinez and it's a possibility."
Funes Mori has played 24 Premier league games for the Blues this season, and is now beginning to establish himself as a first choice centre-back for club and country.
He moved to Goodison Park from River Plate in the summer of 2015, for a deal believed to be around £9.5 million.
Tussles between club and country for their star players are now common place, with more money in the game and more importance placed on results. Clubs are more reluctant to lose one of their key players, especially where in the case of the Olympics it will infringe on actual Premier league game time.
Sky Sports are also reporting that Martino wants to call up other senior players to the Olympic squad, with the likes of Juventus' Paulo Dybala and Atletico Madrid's Luciano Vietto among the names being mentioned.