In addition to operations, concessionaires will also have to widen some stretches.
The two Chinese bidders want to avoid competing against each other while pursuing a bridge contract in Brazil's northeast.
The public works sub-secretary said that the rains in the northern regions caused substantial losses in rural areas.
The planned 450m bridge would connect capital Asunción with the city of Villa Hayes and a tender is planned for June.
President Vázquez also promised that the project will achieve its financial closure next month.
A local firm proposes to modernize and expand the Florencio del Castillo toll highway in San José and Cártago provinces.