"I think Aguirre is going to have to show a keen eye to coordinate the team and pick the best players. Not getting past the first round would be a low blow for Mexican football," the gruff, mustachioed Argentine said.
Mexico, who have reached the second round at the last four World Cups, face a difficult task in Group A, playing hosts South Africa in the opening match on June 11, then 2006 runners-up France and Uruguay.
"There's no doubt that in the national team you've got to be careful what you say," La Volpe, a member of Argentina's 1978 World Cup-winning squad, was quoted on Friday as telling ESPN radio.
"I don't see Aguirre's thing as a surprise, I think his mind is set on carrying on coaching in Europe, he says so now and that's entirely his right."
"If tomorrow I'm asked 'Would you coach the Mexico team?' of course I'd be right there because I believe I have the capacity," said La Volpe, who was in charge from 2002-06.
"I was the only one who lasted (four years), we went to an Olympics, the Confederations Cup, eight or nine players were sold to Europe after my tenure."
