MAXI J1807+132 is an X-ray transient discovered during the decay of an outburst in 2017. We present optical and X-ray monitoring of the source over more than 125 d, from outburst to quiescence. The outburst decay is characterized by the presence of several reflares with a quasi-periodic recurrence time of ˜6.5 d. We detect broad H and He emission lines during outburst, characteristic of transient low-mass X-ray binaries. These emission lines show strong variability from epoch to epoch and, in particular, during the early stages are found embedded into deep and very broad absorption features. The quiescent spectrum shows Hα in emission and no obvious signatures of the donor star. XMM-Newton and Swift spectra can be fitted with standard X-ray models for accreting black holes and neutron stars, although the obtained spectral parameters favour the latter scenario. Conversely, other observables such as the optical/X-ray flux ratio, the likely systemic velocity (γ ˜ -150 km s-1), and the reflares recurrence time suggest a black hole nature. We discuss all the above possibilities with emphasis on the strong similarities of MAXI J1807+132 with short orbital period systems.