The impurity-induced bound states in symmetric and asymmetric chiral p-wave superconducting nanoloops are investigated by numerically solving the Bogoliubov-de Gennes equations self-consistently. When a magnetic impurity is involved, the impurity bound level crosses the Fermi level at some impurity strength for the square loop, accompanied by a current jump at the zero-energy point. The evolution of zero-energy states can be effectively tuned by the located site of a single magnetic impurity. For the asymmetric rectangular loop, the zero mode is easier to be generated when a magnetic impurity is placed at the edge of the short side. In addition, the zero-energy states can be modulated by the threaded magnetic flux. Particularly, for an appropriate strength of the midway magnetic impurity, the zero-energy crossing of the impurity bound level takes place twice with increasing flux.