The task of speech recognition in far-field environments is adversely affected by the reverberant artifacts that elicit as the temporal smearing of the sub-band envelopes. In this paper, we develop a neural model for speech dereverberation using the long-term sub-band envelopes of speech. The sub-band envelopes are derived using frequency domain linear prediction (FDLP) which performs an autoregressive estimation of the Hilbert envelopes. The neural dereverberation model estimates the envelope gain which when applied to reverberant signals suppresses the late reflection components in the far-field signal. The dereverberated envelopes are used for feature extraction in speech recognition. Further, the sequence of steps involved in envelope dereverberation, feature extraction and acoustic modeling for ASR can be implemented as a single neural processing pipeline which allows the joint learning of the dereverberation network and the acoustic model. Several experiments are performed on the REVERB challenge dataset, CHiME-3 dataset and VOiCES dataset. In these experiments, the joint learning of envelope dereverberation and acoustic model yields significant performance improvements over the baseline ASR system based on log-mel spectrogram as well as other past approaches for dereverberation (average relative improvements of 10-24% over the baseline system). A detailed analysis on the choice of hyper-parameters and the cost function involved in envelope dereverberation is also provided.