The directly detected planetary mass companion candidate close to the young, nearby star Fomalhaut is a subject of intense discussion. While the detection of common proper motion led to the interpretation as Jovian-mass companion, later non-detections in the infrared raised doubts. Recent astrometric measurements indicate a belt crossing or highly eccentric orbit for the object, if a companion, making the planetary interpretation potentially even more problematic. In this study we discuss the possibility of Fomalhaut b being a background object with a high proper motion. By analysing the available photometric and astrometric data of the object, we show that they are fully consistent with a neutron star: neutron stars are faint, hot (blue), and fast moving. Neutron stars with an effective temperature of the whole surface area being 112 000–126 500 K (with small to negligible extinction) at a distance of roughly 11 pc (best fit) would be consistent with all observables, namely with the photometric detections in the optical, with the upper limits in the infrared and X-rays, as well as with the astrometry (consistent with a distances of 11 pc or more and high proper motion as typical for neutron stars) and non-detection of pulsation (not beamed). We consider the probability of finding an unrelated object or even a neutron star nearby and mostly co-aligned in proper motion with Fomalhaut A and come to the conclusion that this is definitely well possible.