This report presents a three-dimensional (3-D) magnetoelectrokinetic model to investigate a new approach to magnetic-field assisted dielectrophoresis for ultra-high precision and parallel assembly of ferromagnetic Ni nanowires (NWs) on silicon chips. The underlying assembly methodology relies on a combination of electric and magnetic fields to manipulate single nanowires from a colloidal suspension and yield their assembly on top of electrodes with better than 25 nm precision. The electric fields and the resultant dielectrophoretic forces are generated through the use of patterned gold nanoelectrodes, and deliver long-range forces that attract NWs from farther regions of the workspace and bring them in proximity to the nanoelectrodes. Next, magnetic-fields generated by cobalt magnets, which are stacked on top of the gold nanoelectrodes at their center and pre-magnetized using external magnetic fields, deliver short range forces to capture the nanowires precisely on top of the nanomagnets. The 3-D NanoMagnetoElectrokinetic model, which is built using a finite element code in COMSOL software and with further computations in MATLAB, computes the trajectory and final deposition location as well as orientation for all possible starting locations of a Ni NW within the assembly workspace. The analysis reveals that magnetic-field assisted dielectrophoresis achieves ultra-high precision assembly of NWs on top of the cobalt nanomagnets from a 42% larger workspace volume as compared to pure dielectrophoresis and thereby, establishes the benefits of adding magnetic fields to the assembly workspace. Furthermore, this approach is combined with a strategy to confine the suspension within the reservoir that contains a high density of favorable NW starting locations to deliver high assembly yields for landing NWs on top of contacts that are only twice as wide as the NWs.