The generation of localized magnetic field gradients by on-chip nanomagnets is important for a variety of technological applications, in particular for spin qubits. To advance beyond the empirical design of these nanomagnets, we propose a systematic and general approach based on the micromagnetic formulation of an optimal field gradient source. We study the different field configurations that can be realized and find out quantitatively the most suitable ferromagnetic layer geometries. Using micromagnetic simulations, we then investigate the minimum requirements for reaching magnetic saturation in these nanomagnets. In terms of either longitudinal or transverse field gradient, the results provide an optimal solution for uniform, saturated nanomagnets, where the magnetic material can be selected according to the strength of the external fields that can be used.