Given the speed of viral infection spread, repurposing of existing drugs has been given the highest priority in combating the ongoing COVID-19 pandemic. Only drugs that are already registered or close to registration, and therefore have passed lengthy safety assessments, have a chance to be tested in clinical trials and reach patients quickly enough to help in the current disease outbreak. Here, we have reviewed available evidence and possible ways forward to identify already existing pharmaceuticals displaying modest broad-spectrum antiviral activity which is likely linked to their high accumulation in cells. Several well studied examples indicate that these drugs accumulate in lysosomes, endosomes and biological membranes in general, and thereby interfere with endosomal pathway and intracellular membrane trafficking crucial for viral infection. With the aim to identify other lysosomotropic drugs with possible inherent antiviral activity, we have applied a set of clear physicochemical, pharmacokinetic and molecular criteria on 530 existing drugs. In addition to publicly available data, we have also used our in silico model for the prediction of accumulation in lysosomes and endosomes. By this approach we have identified 36 compounds with possible antiviral effects, also against coronaviruses. For 14 of them evidence of broad-spectrum antiviral activity has already been reported, adding support to the value of this approach. Presented pros and cons, knowledge gaps and methods to identify lysosomotropic antivirals, can help in the evaluation of many drugs currently in clinical trials considered for repurposing to target COVID-19, as well as open doors to finding more potent and safer alternatives.