Lithium Niobate (LN) is one of the most intensively and exploited materials in fundamental and applied optics. Lithium Niobate is a ferroelectric material that exhibits spontaneous electric polarization that can be switched to its symmetry equivalent states with applied electric field. It is known that ferroelectricity is suppressed at the nano-scale, due to depolarization fields arising from the bound charges at the surface. For example, ferroelectricity in BaTiO3 nanoparticles disappears below a critical size (40 nm). On the other hand, recent works have shown that ferromagnetism occurs in nanoparticles of the otherwise non-magnetic oxides, but decreases with increasing particle size. Magnetism in these nanoparticles, considered to arise from vacancies at the surface, is suggested to be a universal phenomenon. A recent finding of ferroelectricity in much smaller (12 nm) nanoparticles of BaTiO3 motivated us to explore the simultaneous occurrence of ferromagnetism and ferroelectricity in nanocrystalline LiNbO3. The dielectric properties of nanostructured LiNbO3 are studied by analyzing the low-loss region of the electron energy loss spectroscopy (EELS) in a transmission electron microscope.