Context. Observations of reconnection jets in the solar corona are emerging as a possible diagnostic for studying highly elusive coronal heating. Such jets, and in particular those termed nanojets, can be observed in coronal loops and have been linked to nanoflares. However, while models successfully describe the bilateral post-reconnection magnetic slingshot effect that leads to the jets, observations reveal that nanojets are unidirectional or highly asymmetric, with only the jet travelling inward with respect to the coronal loop's curvature being clearly observed. Aims. The aim of this work is to address the role of the curvature of the coronal loop in the generation and evolution of asymmetric reconnection jets. Methods. We first use a simplified analytical model in which we estimate the post-reconnection tension forces based on the local intersection angle between the pre-reconnection magnetic field lines and their post-reconnection retracting length towards new equilibria. Second, we use a simplified numerical magnetohydrodynamic (MHD) model to study how two opposite propagating jets evolve in curved magnetic field lines. Results. Through our analytical model, we demonstrate that in the post-reconnection reorganised magnetic field, the inward directed magnetic tension is inherently stronger (by up to three orders of magnitude) than the outward directed one and that, with a large enough retracting length, a regime exists where the outward directed tension disappears, leading to no outward jet at large, observable scales. Our MHD numerical model provides support for these results, proving also that in the subsequent time evolution the inward jets are consistently more energetic. The degree of asymmetry is also found to increase for small-Angle reconnection and for more localised reconnection regions. Conclusions. This work shows that the curvature of the coronal loops can play a major role in the asymmetry of the reconnection jets and that inward directed jets are more likely to occur and are more energetic than the corresponding outward directed ones.