Vazquez said the formal announcement of the bid would take place during a visit to Uruguay by Argentine counterpart Mauricio Macri on August 30.
The move coincides with Uruguay’s 2018 World Cup qualifier against Argentina in Montevideo on August 31.
The joint bid between the two South American neighbours had long been signaled.
Uruguay, the hosts of the inaugural World Cup in 1930, is hoping to win the rights to the tournament with Argentina to mark the centenary of the event.
Both Uruguay and Argentina have won the World Cup twice before, with Uruguay taking the inaugural tournament and again in 1950.
Argentina won the tournament in 1978 on home soil, and again in Mexico in 1986.
South America last staged the World Cup in Brazil in 2014 and any bid for 2030 is likely to face stiff competition from the Asian region, where China is expected to be the front-runner to stage the finals.
The next World Cup takes place in Russia, with Qatar staging the event in 2022.
A joint United States-Mexico-Canada bid is the favorite to win the 2026 tournament, with only one other country, Morocco, so far expressing an interest in entering the bidding race.