In the last decade particular emphasis has been placed on the problem of optically controlled energy transfer in quantum systems near plasmonic nanostructures. It has also been shown that strong quantum coherence can lead to highly enhanced energy transfer between two molecules in a nanophotonic environment. Recent studies have also shown that using transition metal dichalcogenide nanostructures can achieve strong coupling in quantum systems, like molecules, at the nanoscale. In this work, we present a theoretical investigation of the role of coherence in the efficiency of energy transfer in a composite system of two molecules, a donor and an acceptor, located at the opposite side of a MoS₂ nanodisk. We consider the molecules as two-level quantum systems, and, based on the Lindblad master equation combined with classical electromagnetic Green's tensor methodology, study the energy transfer efficiency and dynamics. Taking into consideration the dissipation in the donor and the charge separation rate, we focus on the transfer dynamics of the two molecules, with and without quantum coherence, for different distances and dipole orientations with respect to the surface of the MoS₂ nanodisk. The presence of the MoS₂ nanodisk enhances the relaxation rate, the coherent and the incoherent terms of coupling coefficients of the molecules, thus affecting their dynamic response. Our results show high efficiency energy transfer between the two molecules in the presence of strong coherence for small distances from the MoS₂ nanodisk. Also, for specific dipole polarization, small dissipation in the donor and strong charge separation rate, we observe ultrafast, in the scale of picosecond, and largely improved energy transfer process compared with the case without coherence. The results are expected to have a positive impact on the coherent techniques of energy transfer for the design of new, improved and useful harvesting light devices in nanotechnology.