Gaich scored three goals for Argentina at the Under-20 World Cup earlier this summer as his country crashed out at the last-16 stage.
Marca claim the 20-year-old is being chased by Everton and Serie A club Genoa.
He has made just a handful of appearances for Argentine side San Lorenzo.
Pablo Caro, Gaich’s agent, revealed his client would favour a move to a European club.
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He said: “We spoke with clubs in Italy. The Everton issue isn’t clear yet.