The Football Association of Wales is in talks with Argentina about hopes of at least one friendly in 2015.
It raises the prospect of the world's most expensive player, Welshman Gareth Bale, facing arguably the world's best player, Argentina's Lionel Messi.
Next year will mark the 150th anniversary of Welsh settlers arriving in the southern region of Patagonia.
Some 150 Welsh people sailed from Liverpool on the Mimosa to South Argentina in 1865.
Bale and Messi's club sides Real Madrid and Barcelona meet on Saturday in the first El Clasico of the Spanish season.
The last time Wales played against Argentina in a friendly match at the Millennium Stadium was in 2002.
Craig Bellamy scored for Wales, but Julio Ricardo Cruz secured a 1-1 draw for Argentina.
That was only the second meeting between the two countries - Argentina beat Wales 1-0 in the first in the Kirin Cup in Japan in 1992.
One game could be held in Wales and the other one could be held in Argentina.
Wales and Argentina's international rugby union teams have been intermittent rivals.
On tour to the South American country in 2006, Wales went to the site of the settlers' landing in Patagonia and lost the Test in Puerto Madryn 27-25.