The new Coronavirus (SARS-CoV-2) is the cause of a serious infection in the respiratory tract called COVID-19. Structures of the main protease of SARS-CoV-2 (M(pro)), responsible for the replication of the virus, have been solved and quickly made available, thus allowing the design of compounds that could interact with this protease and thus to prevent the progression of the disease by avoiding the viral peptide to be cleaved, so that smaller viral proteins can be released into the host's plasma. These structural data are extremely important for in silico design and development of compounds as well, being possible to quick and effectively identify potential inhibitors addressed to such enzyme's structure. Therefore, in order to identify potential inhibitors for M(pro), we used virtual screening approaches based with the structure of the enzyme and two compounds libraries, targeted to SARS-CoV-2, containing compounds with predicted activity against M(pro). In this way, we selected, through docking studies, the 100 top-ranked compounds, which followed to subsequent studies of pharmacokinetic and toxicity predictions. After all the simulations and predictions here performed, we obtained 10 top-ranked compounds that were again in silico analyzed inside the M(pro) catalytic site, together some drugs that are being currently investigated for treatment of COVID-19. After proposing and analyzing the interaction modes of these compounds, we submitted one molecule then selected as template to a 2D similarity study in a database containing drugs approved by FDA and we have found and indicated Apixaban as a potential drug for future treatment of COVID-19.