Unique structural and optical properties of atomically thin transition metal dichalcogenides (TMDs) enable in principle their efficient coupling to photonic cavities having the optical mode volume below the diffraction limit. So far, this has only been demonstrated by coupling TMDs with plasmonic modes in metallic nano-structures, which exhibit strong energy dissipation limiting their potential applications in devices. Here, we present an alternative approach for realisation of ultra-compact cavities interacting with two-dimensional semiconductors: we use mono- and bilayer TMD WSe2 coupled to low-loss high-refractive-index gallium phosphide (GaP) nano-antennas. We observe a photoluminescence (PL) enhancement exceeding 104 compared with WSe2 placed on the planar GaP, and trace its origin to a combination of enhancement of the spontaneous light emission rate, favourable modification of the PL directionality and enhanced optical excitation efficiency, all occurring as a result of WSe2 coupling with strongly confined photonic modes of the nano-antennas. Further effect of the coupling is observed in the polarisation dependence of WSe2 PL, and in the Raman scattering signal enhancement exceeding 103. Our findings reveal high-index dielectric nano-structures as a promising platform for engineering light-matter coupling in two-dimensional semiconductors.