Modern brain computer interface (BCI) applications use information obtained from the user's electroencephalogram (EEG) to estimate the mental states. Selecting an optimal subset of the EEG channels instead of using all of them is especially important for ambulatory EEG where the user is mobile due to reduced data communication and computational load requirements. In addition, elimination of irrelevant sensors improves the robustness of the classification system by reducing dimensionality. In this paper, we propose a filter approach for EEG channel selection using mutual information (MI) maximization. This method ranks the EEG channels, such that the MI between the selected sensors and class labels is maximized. This selection criterion is known to reduce classification error. We employ a computationally efficient approach for MI estimation and EEG channel ranking. This approach is illustrated on EEG data recorded from three subjects performing two mental tasks. Experiment results show that the proposed approach works well and the position of the selected channels using the proposed method is consistent with the expected cortical areas for the mental tasks.