In this paper, a novel technique based on signal processing of breath sounds during wakefulness for prediction of obstructive sleep apnea (OSA) is proposed. We recorded tracheal breath sounds of 35 people with various severity of OSA and 17 non-apneic individuals; the breath sounds were recorded in supine and upright positions during both nose and mouth breathing at medium flow rate. Power spectrum, Kurtosis and Katz fractal dimension of the recorded signals in every posture and breathing maneuver were calculated. We used one-way ANOVA to select the features with most significant differences between the groups followed by the Maximum Relevancy Minimum Redundancy (mRMR) method to reduce the number of characteristic features to three, and investigated the separability of the groups based on the three selected features. The results are encouraging for classification of patients using the selected features. Once being verified on a larger population, the proposed method offers a fast, simple and non-invasive screening tool for prediction of OSA during wakefulness.