There is an immediate need to discover treatments for COVID-19, the pandemic caused by the SARS-CoV-2 virus. Standard small molecule drug discovery workflows that start with library screens are an impractical path forward given the timelines to discover, develop, and test clinically. To accelerate the time to patient testing, here we explored the therapeutic potential of small molecule drugs that have been tested to some degree in a clinical environment, including approved medications, as possible therapeutic interventions for COVID-19. Motivating our process is a concept termed polypharmacology, i.e. off-target interactions that may hold therapeutic potential. In this work, we used Ligand Design, our deep learning drug design platform, to interrogate the polypharmacological profiles of an internal collection of small molecule drugs with federal approval or going through clinical trials, with the goal of identifying molecules predicted to modulate targets relevant for COVID-19 treatment. Resulting from our efforts is PolypharmDB, a resource of drugs and their predicted binding of protein targets across the human proteome. Mining PolypharmDB yielded molecules predicted to interact with human and viral drug targets for COVID-19, including host proteins linked to viral entry and proliferation and key viral proteins associated with the virus life-cycle. Further, we assembled a collection of prioritized approved drugs for two specific host-targets, TMPRSS2 and cathepsin B, whose joint inhibition was recently shown to block SARS-CoV-2 virus entry into host cells. Overall, we demonstrate that our approach facilitates rapid response, identifying 30 prioritized candidates for testing for their possible use as anti-COVID drugs. Using the PolypharmDB resource, it is possible to identify repurposed drug candidates for newly discovered targets within a single work day. We are making a complete list of the molecules we identified available at no cost to partners with the ability to test them for efficacy, in vitro and/or clinically.