When the matter from a companion star is accreted towards the central compact accretor, i.e. a black hole (BH) or a neutron star (NS), an accretion disc and a jet outflow will form, providing bight X-ray and radio emission, which is known as X-ray binaries (XRBs). In the low/hard state, there exist disc-jet couplings in XRBs, but it remains uncertain whether the jet power comes from the disc or the central accretor. Moreover, BHXRBs have different properties compared with NSXRBs: quiescent BHXRBs are typically two to three orders of magnitude less luminous than NSXRBs in X-ray, whereas BHXRBs are more radio loud than NSXRBs. In observations, an empirical correlation has been established between radio and X-ray luminosity, $L_{rm R} propto L_{rm X}^b$, where $bsim 0.7$ for BHXRBs and $b sim 1.4$ for non-pulsating NSXRBs. However, there are some outliers of BHXRBs showing unusually steep correlation as NSXRBs at higher luminosities. In this work, under the assumption that the origin of jet power is related to the internal energy of the inner disc, we apply our magnetized, radiatively efficient thin disc model and the well-known radiatively inefficient accretion flow model to NSXRBs and BHXRBs. We find that the observed radio/X-ray correlations in XRBs can be well understood by the disc-jet couplings.