A method to manipulate magnetization reversal in core-shell nanostructures is presented. The focus is on cylindrical multilayer structures comprising of an inner conductor wire covered by two shells: (i) an intermediate non-conducting and non-magnetic shell and (ii) a nanotube made of an outer ferromagnetic layer. The properties of the magnetization reversal of the ferromagnetic phase are investigated when a circular Oersted field is generated by applying an electric current through the inner wire. Coercive fields and remanent magnetization as functions of the circular field strength are explored. By means of a simple analytical model and OOMMF simulations, once the current is turned on, two key results have been found: (i) A manipulable axial demagnetization, that is, a magnetization transition from the quasi uniform alignment to a flux closure circular configuration when the circular field strength is above a critical field; and (ii) a quadratic reduction of the coercivity on the circular field strength, in the case that the nanotube magnetization is switched by an applied magnetic field along the tube axis and further assisted by a circular Oersted field. It is found that in this kind of structures, Oersted field assisted magnetization reversal (OAMR) can be an alternative way to reduce coercivity, as required by the magnetic storage industry and currently performed with heat assisted techniques.