The South American neighbours are counting on sentimental support with Uruguay hosting the first FIFA World Cup in 1930.
Argentina sports secretary Carlos Mac Allister said in an interview that the presidents of both countries and leaders of the two national football federations had agreed to move ahead.
Politicians will face questions about potentially spending billions on football stadiums. South American neighbours Brazil hosted the 2014 FIFA World Cup and 2016 Olympics and were roundly criticised for building 'white elephant' sports venues and ignoring run-down schools and hospitals.
Argentina (1978 and 1986) and Uruguay (1930 and 1950) have each won the FIFA World Cup twice.