Measurement of neural tracking of natural running speech from the electroencephalogram (EEG) is an increasingly popular method in auditory neuroscience and has applications in audiology. The method involves decoding the envelope of the speech signal from the EEG signal, and calculating the correlation with the envelope of the audio stream that was presented to the subject. Typically EEG systems with 64 or more electrodes are used. However, in practical applications, set-ups with fewer electrodes are required. Here, we determine the optimal number of electrodes, and the best position to place a limited number of electrodes on the scalp. We propose a channel selection strategy based on an utility metric, which allows a quick quantitative assessment of the influence of a channel (or a group of channels) on the reconstruction error. We consider two use cases: a subject-specific case, where the optimal number and position of the electrodes is determined for each subject individually, and a subject-independent case, where the electrodes are placed at the same positions (in the 10-20 system) for all the subjects. We evaluated our approach using 64-channel EEG data from 90 subjects. In the subject-specific case we found that the correlation between actual and reconstructed envelope first increased with decreasing number of electrodes, with an optimum at around 20 electrodes, yielding 29% higher correlations using the optimal number of electrodes compared to all electrodes. This means that our strategy of removing electrodes can be used to improve the correlation metric in high-density EEG recordings. In the subject-independent case, we obtained a stable decoding performance when decreasing from 64 to 22 channels. When the number of channels was further decreased, the correlation decreased. For a maximal decrease in correlation of 10%, 32 well-placed electrodes were sufficient in 91% of the subjects.