Source　localization　in　reverberant　environments　has　been　a　prominent　research　topic　in　the　past　two　decades.　In　this　paper,　instead　of　the　commonly　employed　time-frequency　(TF)　bin　based　methods　which　rely　on　empirically　selected　threshold　values,　we　leverage　the　microphone　array　signal　model　comprising　an　early　reverberant　component　and　a　late　reverberant　component,　to　propose　a　novel　method　for　the　source　localization　problem　in　reverberant　environments.　Our　proposed　criterion　involves　the　joint　removal　of　the　late　reverberant　component　using　the　multi-channel　linear　prediction　(MCLP)　filter,　while　estimating　the　directions　of　arrival　(DOAs)　of　the　actual　sources　using　the　early　component　signals.　By　applying　the　azimuth　sparsity　constraint,　the　true　DOA　can　be　estimated　with　high　resolution　and　free　from　the　interference　of　the　early　reflections.　To　solve　the　proposed　criterion,　DOAs,　source　signals,　and　MCLP　filter　coefficients　are　estimated　by　alternative　iterations.　Additionally,　we　present　a　source　localization　criterion　specifically　designed　for　the　single　source　scenario　as　a　special　case　of　the　multiple　sources　scenario.　Finally,　a　source　number　estimation　method　and　a　postprocessing　procedure　are　discussed　for　searching　the　global　solutions　to　our　proposed　criteria.　Evaluations　with　both　simulated　and　realistic　data　demonstrate　the　advantages　of　our　proposed　methods　over　the　baseline　methods.