Blind multichannel speech dereverberation methods based on multichannel linear prediction (MCLP) estimate the dereverberated speech component without any knowledge of the room acoustics by estimating and subtracting the undesired reverberant component from the reference microphone signal. In this paper we present a general framework for incorporating sparsity in the time-frequency domain into MCLP-based speech dereverberation. The presented framework enables to use either a wideband or a narrowband signal model with either an analysis or a synthesis sparsity prior for the desired speech component and generalizes stateof- the-art MCLP-based speech dereverberation methods, which is shown both analytically as well as using simulations.