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The Australian newspaper said the clash would take place in early June at the 100,000-capacity Melbourne Cricket Ground, pitting Barcelona superstars Messi and Neymar against each other.
One team would likely stay on and play Australia ahead of the Socceroos participation in the Confederations Cup in Russia later that month, it added.
Football Federation Australia told AFP it had nothing to say on the matter, with the Victorian state government echoing similar sentiments.
Brazil won two editions of the occasional friendly series against Argentina in 2011 and 2012, and again in 2014 when they faced off in Beijing.
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