In this paper, we propose a novel study concerning the future use of a zero-airgap induction motor in applications related to transmission oil pumps. The name of the machine comes from the fact that the rotor touches the stator as it spins. The use of such an eccentric motor provides the possibility to remove the mechanical part that is typically found in the transmission oil pump, increasing its efficiency in this way. We focused on determining the optimum variant of a zero-airgap small power induction motor from the point of view of the electrical and mechanical performance. As such, 18 topologies of induction motors with various numbers of pole pairs and rotor bars were designed and numerically analyzed. For the best variant from each category, different eccentricities were considered to evaluate this effect over the performances of the motors. For the best candidate, various analyses were performed in order to demonstrate the validity of this solution for the proposed application. Elements regarding the thermal analysis of this structure are also presented here.