The study identifies universities and areas of knowledge where there are better prospects for effective and successful international cooperation and recommends a set of actions to address deficiencies in the universities. It indicates that the internationalization of Brazilian Universities requires gradual qualification of institutions aiming at achieving success in the formatting of our first World Class Universities (WCU). An advance on this urgent challenge can be facilitated by the involvement of the most qualified postgraduate programs (concepts 6 and 7 of CAPES) that already have a certain level of internationalization. An action in this direction should aim at promoting better university performance in order to avoid the risk of Brazil acting in a subservient manner, a common situation in the vast majority of less developed countries with regard to international cooperation. Clearly, this is a perspective of true international cooperation aimed at promoting the development of complete collaborative research projects through specific financial support for initiatives of shared scientific and technological interaction, which is far ahead of the models used until now by the simple granting agencies designed for training grants abroad. Although it is expected that there will certainly be profound changes in the global context with regard to the functioning of universities in the post-COVID-19 scenario, the surviving institutions will need, with more reason, to be attuned to the prospect of strong international interaction. This becomes even more relevant considering the extraordinary advances in modern technologies focused on digitization and the domain of knowledge in algorithms, big data, artificial intelligence and other technologies and their applicability.