Mexico hosted the 1970 and 1986 World Cups and a successful bid for the 2026 finals would make the country the first to host the global showpiece event three times.
"Mexico was a great host in '70 and '86, so we are indeed going to fight (for the right), we want to have a World Cup (again), there will be a strong competition with the United States," Mexican Football Federation president Compean said.
"Mexico's football infrastructure keeps growing and that World Cup can be feasible for Mexico."
The 1950 World Cup hosts Brazil stage their second finals in 2014. Russia won the 2018 bid, while Qatar will stage the 2022 finals.
"FIFA is always more demanding with all the structures that are needed. The great competitor (for 2026) is the United States, which has great resources, great stadiums, triple the population we have and all that counts," Compean said.
The US held the finals for the first time in 1994.
Other countries to have held the finals twice are Italy (1934 and 1990), France (1938 and 1998) and Germany (1974, as West Germany, and 2006).
Compean said Mexico's national team would still win the 2026 World Cup, even if the US were awarded hosting rights.
"Assuming the United States were to get the (2026) World Cup, we would still win because on a sporting level we wouldn't have to face each other in the qualifiers," he said.
"We're three hours from the border and we have millions of nationals living on the other side so we'd be playing as a home team."