This paper presents a power-strength-based selective forwarding (PSF) mechanism to efficiently flood route requests (RREQs) during route discovery in multihop cellular networks (MCNs). In PSF, each mobile station utilizes the received power strength, instead of the connectivity or overheard information, to determine whether it has to be a forwarding participant or not. It reduces the signaling overhead and prevents unnecessary interference during route discovery. An analytical method is proposed to set the power thresholds required to ensure a target connectivity probability. The accuracy of the proposed method was verified via computer simulation. Simulation results show that the proposed PSF mechanism can significantly reduce the number of RREQs while ensuring the connectivity probability.