The country's first-ever PPP contract was awarded in July to a Mexican-Guatemalan consortium.
Ultra right-wing candidate Jair Bolsonaro won the first round in Brazil's presidential election and gave a major boost to his small PSL party in congress.
The fund will count with the participation of pension funds and institutional investors.
The country's transport minister will meet executives from the IDB, World Bank, CitiBank and other lenders to discuss financing alternatives.
The PPP project entails building a new 18,000m2 terminal for Cartagena airport, as well as modernizing 5,000m2 of the existing terminal.
The Brazilian concessionaires are being investigated in relation to an alleged bribery scheme.