The emergence of SARS-CoV-2 has prompted a worldwide health emergency. There is an urgent need for therapeutics, both through the repurposing of approved drugs and the development of new treatments. In addition to the viral drug targets, a number of human drug targets have been suggested. In theory, targeting human proteins should provide an advantage over targeting viral proteins in terms of drug resistance, which is commonly a problem in treating RNA viruses. This paper focuses on the human protein TMPRSS2, which supports coronavirus life cycles by cleaving viral spike proteins. The three-dimensional structure of TMPRSS2 is not known and so we have generated models of the TMPRSS2 in the apo state as well as in complex with a peptide substrate and putative inhibitors to aid future work. Importantly, many related human proteases have 80% or higher identity with TMPRSS2 in the S1-S1' subsites, with plasminogen and urokinase-type plasminogen activator (uPA) having 95% identity. We highlight 376 approved, investigational or experimental drugs targeting S1A serine proteases that may also inhibit TMPRSS2. Whilst the presence of a relatively uncommon lysine residue in the S2/S3 subsites means that some serine protease inhibitors will not inhibit TMPRSS2, this residue is likely to provide a handle for selective targeting in a focused drug discovery project. We discuss how experimental drugs targeting related serine proteases might be repurposed as TMPRSS2 inhibitors to treat coronaviruses.