Potassium (K) is an element almost as abundant as sodium and with a low standard redox potential comparable to Li/Li+, which makes the investigation of K-based batteries a field which has been gaining interest lately. A group of possible cathode materials which has not been studied in detail yet are crystalline vanadium oxides, although their excellent metal insertion properties are known for a variety of other alkali and alkaline earth elements. In this study, four promising vanadium oxide phases (layered α-V2O5 and β-V2O5, non-layered bronze- and rutile-type VO2) are investigated from first principles as potential electrode materials for K ion batteries. Insertion energetics and diffusion barriers at the dilute limit were computed and changes in electronic structure upon K insertion (densities of states, charge density distributions) analyzed. We investigated the influence of dispersion corrections on the potassiated layered and non-layered vanadium oxides in order to choose an appropriate computational setup for all phases. Our results show that the metastable β-V2O5 provides the lowest (strongest) insertion energies for K and the lowest diffusion barriers compared to orthorhombic α-V2O5, bronze- and rutile VO2. While three of these phases show an energetically favorable potassiation and relatively small diffusion barriers, VO2(R) is predicted to be incapable of electrochemical K incorporation.