The Catholic leader was handed the yellow T-shirt by the Governor-General of Australia Sir Peter Cosgrove during a meeting at the Vatican on Monday.
Speaking through the translator, the South American-born pope asked: "Does he [I] have to put in on?", to which Sir Peter replied: "No, no, no. Not now. When you're watching the game".
Last year, Francis, who comes from Argentina, was presented by the former President of Peru Pablo Kuczynski with a football jersey of the national football team.
A statement released by the Vatican press office said global and regional migration, and climate change were discussed.
A statement continued: "Mention was also made of the role of the Church in Australian society, and the current discussion on the protection of minors and vulnerable people, reiterating the commitment of all members of the Church in this regard.
"Attention then turned to the social situation of the country, and to the question of peace and stability in the entire region of the Pacific and of Asia."
Australia's clash with Peru kicks off at 3pm UK time inside the First Olympic Stadium in Sochi, Russia.
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