The Migdal effect is attracting interest because of the potential to enhance the sensitivities of direct dark matter searches to the low-mass region. In spite of its great importance, the Migdal effect has not been experimentally observed yet. A realistic experimental approach towards the first observation of the Migdal effect in the neutron scattering was studied with Monte Carlo simulations. In this study, the potential background rate was studied together with the event rate of the Migdal effect by a neutron source. It was found that a table-top-sized~ (30 cm)3 positionsensitive gaseous detector filled with argon or xenon target gas can detect characteristic signatures of the Migdal effect with sufficient rates (O(102 ~ 103) events per day). A simulation result of a simple experimental set-up showed two significant background sources, namely the intrinsic neutrons and the neutron-induced gamma-rays. It is found that the intrinsic neutron background rate for the argon gas is at an acceptable level and some future study of the reduction of the gamma-rays from the laboratory would make the observation of the Migdal effect possible. The background for the xenon gas, on the other hand, is found to be much more serious than for the argon gas. Future works on the isotope separation as well as the reduction of the gamma-rays from the detector and laboratory will be needed before the Migdal effect can be observed for the xenon gas case.