In 1930, Uruguay, the then double Olympic champions, beat Argentina 4-2 in the showpiece match at the Centenario stadium in Montevideo in front of a crowd of more than 80,000.
"FIFA wishes to celebrate the World Cup's 100 years in Argentina and Uruguay, I can confirm that," said Grondona, the senior vice-president of world soccer's governing body.
"[An agreement] has been signed by the two associations (AFA and Uruguay's AUF). What will we do? We'll see but surely something of quality," Grondona told Argentina's Radio 10.
The only co-hosted World Cup finals so far were organised by Japan and South Korea in 2002.
Any future joint bid must have one organising committee, unlike the 2002 Asian World Cup which had separate Japanese and Korean committees.
The 2014 finals are being held in Brazil, Russia won the vote for the 2018 tournament and Qatar, a tiny nation with no football pedigree and extremely high temperatures in mid-year, was controversially chosen to stage the 2022 tournament.
A joint Argentine-Uruguayan bid for 2030 is backed by the South American Football Confederation (CONMEBOL).
Uruguay's Tourism and Sports ministry formally approached FIFA president Sepp Blatter at the start of the 2010 World Cup finals in South Africa to propose the joint bid.
Blatter has since said on several occasions, especially during visits to Latin America, that he liked the idea of the centenary tournament being held by Uruguay and Argentina.
However, the voting system has changed since controversy surrounded the decision to award the finals to Russia and Qatar.
The 24-man executive committee had voted on bids until last year but now the 209-member FIFA Congress will decide which countries host future World Cup tournaments.
When Uruguay held the inaugural tournament only 13 teams took part but the small South American country does not have the stadiums or infrastructure to stage a modern, 32-team finals.
With the involvement of big neighbours Argentina, who staged and won the 1978 finals, such an enterprise is more feasible.
