General relativistic quantum interference effects in a slowly rotating NUT space–time, such as the Sagnac effect and the phase shift effect of interfering particles in a neutron interferometer, are considered. It was found that in the case of the Sagnac effect, the influence of the NUT parameter is becoming important due to the fact that the angular velocity of the locally nonrotating observer must be larger than the one in the Kerr space–time. In the case of neutron interferometry, it is found that due to the presence of the NUT parameter, an additional term in the phase shift of interfering particles emerges. This term can be, in principle, detected by a sensitive interferometer and the derived results could be further used in experiments to detect the gravitomagnetic charge. Finally, as an example, we apply the obtained results to the calculation of the UCN (ultra-cold neutrons) energy level modification in a slowly rotating NUT space–time.