The decision directed (DD) approach is widely used to determine a priori SNR from noisy speech signals. In conventional speech enhancement systems with a DD approach, a priori SNR is estimated by using only the magnitude components and consequently follows a posteriori SNR with one frame delay. We propose a phase-dependent two-step a priori SNR estimator based on the minimum mean square error (MMSE) in the log-mel spectral domain so that we can consider both magnitude and phase information, and it can overcome the performance degradation caused by one frame delay. From the experimental results, the proposed estimator is shown to improve the output SNR of enhanced speech signals by 2.3 dB compared to the conventional DD approach-based system.