  Free-floating planets are recently drawing a special interest of the
scientific community. Gravitational microlensing is up to now the exclusive
method for the investigation of free-floating planets, including their spatial
distribution function and mass function. In this work, we examine the
possibility that the future Euclid space-based observatory may allow to
discover a substantial number of microlensing events caused by free-floating
planets. Based on latest results about the free-floating planet mass function
in the mass range $[10^{-5}, 10^{-2}]M_{\odot}$, we calculate the optical depth
towards the Galactic bulge as well as the expected microlensing rate and find
that Euclid may be able to detect hundreds to thousands of these events per
month. Making use of a synthetic population, we also investigate the
possibility of detecting parallax effect in simulated microlensing events due
to free-floating planets and find a significant efficiency for the parallax
detection that turns out to be around 30%.
