We present a detailed study on the kinematics of metal-rich stars with and without planets, and their relation to the Hyades, Sirius and Hercules dynamical streams in the solar neighbourhood. Accurate kinematics have been derived for all the stars belonging to the CORALIE planet search survey. We used precise radial velocity measurements and CCF parameters from the CORALIE database, and parallaxes, photometry and proper motions from the HIPPARCOS and Tycho-2 catalogues. The location of stars with planets in the thin or thick discs has been analysed using both kinematic and chemical constraints. We compare the kinematic behaviour of known planet-host stars to the remaining targets belonging to the volume-limited sample, in particular to its metal-rich population. The high average metallicity of the Hyades stream is confirmed. The planet-host targets show a kinematic behaviour similar to that of the metal-rich comparison subsample, rather than to that of the comparison sample as a whole, thus supporting a primordial origin for the metal excess observed in stars with known planetary companions. According to the scenarios proposed as an explanation for the dynamical streams, systems with giant planets could have formed more easily in metal-rich inner Galactic regions and then been brought into the solar neighbourhood by dynamical streams.