Aims. We study the period of the Slichter mode (vibrational mode of the inner core of a planet) of Mercury in relation to its interior structure and assess the possibility to observe this mode with the probes MESSENGER and BepiColombo. Methods. The methodology of Grinfeld & Wisdom (2005, Phys. Earth Planet. Int., 151, 77) for the determination of the period of the polar Slichter modes of a planetary interior consisting of three homogeneous layers is generalized to models with an arbitrary but finite number of layers. Slichter modes periods are calculated for a large set of interior structure models of Mercury. We study the possible excitation of Slichter modes by a colllision with a meteoroid and estimate the minimal size of the meteoroid that could lead to a detection of these modes by BepiColombo. Results. The Slichter mode period obtained is on the order of several hours. Observation of the Slichter mode of Mercury allows constraining the inner core. An impact by a meteoroid with a radius of at least 100 m could excite the Slichter mode to a level observable by BepiColombo (assuming that the Slichter mode is the only excited mode), but since the estimated damping time of the Slichter mode is well below the average time between impacts of at least that size such an impact must have occured recently (less than 0.5 My ago).