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Marca claimed that Puyol, 32, decided last November to retire from international football after the Soccer World Cup, which Spain won on Sunday by beating the Netherlands 1-0 in Johannesburg.
Puyol was fundamental in La Roja's triumph, and scored the winning goal in the semi-final against Germany.
According to Marca, he now wants to concentrate on playing for Liga champions Barcelona, where he is captain and idol of the fans.
Puyol has turned out 90 times for the national team, since making his debut in a friendly against the Netherlands in November 2000 as an attacking right-back.
He played at right-back at the 2002 World Cup finals, then as centre-back at the 2006 and 2010 World Cups, as well as at Euro 2004 and Euro 2008.