The coronavirus disease 2019 pandemic accelerated drug/vaccine development processes, integrating scientists all over the globe to create therapeutic alternatives against this virus. In this work, we have collected information regarding proteins from SARS-CoV-2 and humans and how these proteins interact. We have also collected information from public databases on protein–drug interactions. We represent this data as networks that allow us to gain insights into protein–protein interactions between both organisms. With the collected data, we have obtained statistical metrics of the networks. This data analysis has allowed us to find relevant information on which proteins and drugs are the most relevant from the network pharmacology perspective. This method not only allows us to focus on viral proteins as the main targets for COVID-19 but also reveals that some human proteins could be also important in drug repurposing campaigns. As a result of the analysis of the SARS-CoV-2–human interactome, we have identified some old drugs, such as disulfiram, auranofin, gefitinib, suloctidil, and bromhexine as potential therapies for the treatment of COVID-19 deciphering their potential complex mechanism of action.