Here, we investigate the possibility of a significant atmospheric contribution to the tidal dissipation of the Phobos-Mars system. We apply the classical tidal theory and we find that most of the gravitational forcing is projected onto the first symmetric Hough mode which has an equivalent depth of about 57 km and is significantly trapped in the vertical. Therefore, no significant dissipation occurs through the vertical propagation of energy and subsequent breaking of the tidal wave as the wave amplifies with height. Alternatively, from the energy stored in the first trapped mode we estimate that the time scale required for the dissipative mechanisms to account for the total dissipation of the tides is of order 102 s. This time scale is unrealistically short, since it would contradict observations of propagating thermal tides in Mars atmosphere. Therefore we conclude that the dissipation of the tidal potential that explains the observed acceleration of Phobos most likely occurs within the solid planet.