The performance of the deep neural networks (DNNs) based monaural speech enhancement methods is still limited in real room environments, particularly for the speaker-independent case. The surface reflections and unseen speakers increase the challenge in the estimation of sources from reverberant noisy speech mixtures. To address these issues, we propose a two-stage approach using long short-term memory (LSTM) networks. In the first stage, the dereverberation mask (DM) is obtained by using a trained LSTM, which aims to dereverberate the noisy speech mixture. In the second stage, the ideal ratio mask (IRM) is estimated by the second trained LSTM, which is exploited to separate the desired speech signal from the dereverberated speech mixture. The signal-to-distortion ratio (SDR) shows the efficacy of the LSTMs over DNNs.