This study aimed at evaluating whether people with a normal cognitive function can be discriminated from subjects with a mild impairment of cognitive function based on a set of acoustic features derived from spontaneous speech. Voice recordings from 90 Italian subjects (age >65 years; group 1: 47 subjects with MMSE>26; group 2: 43 subjects with 20≤ MMSE ≤26) were collected. Voice samples were processed using a MATLAB-based custom software to derive a broad set of known acoustic features. Linear mixed model analyses were performed to select the features able to significantly distinguish between groups. The selected features (% of unvoiced segments, duration of unvoiced segments, % of voice breaks, speech rate, and duration of syllables), alone or in addition to age and years of education, were used to build a learning-based classifier. The leave-one-out cross validation was used for testing and the classifier accuracy was computed. When the voice features were used alone, an overall classification accuracy of 0.73 was achieved. When age and years of education were additionally used, the overall accuracy increased up to 0.80. These performances were lower than the accuracy of 0.86 found in a recent study. However, in that study the classification was based on several tasks, including more cognitive demanding tasks. Our results are encouraging because acoustic features, derived for the first time only from an ecologic continuous speech task, were able to discriminate people with a normal cognitive function from people with a mild cognitive decline. This study poses the basis for the development of a mobile application performing automatic voice analysis on-the-fly during phone calls, which might potentially support the detection of early signs of functional cognitive decline.