We study theoretically the nonequilibrium exciton transport in monolayer transition metal dichalcogenides. We consider the situation where excitons interact with nonequilibrium phonons, e.g., under the conditions of localized excitation where a "hot spot" is formed. We develop the theory of the exciton drag by the phonons and analyze in detail the regimes of diffusive propagation of phonons and ballistic propagation of phonons where the phonon wind is generated. We demonstrate that a halolike spatial distribution of excitons akin observed in [Phys. Rev. Lett. 120, 207401 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.207401] can result from the exciton drag by nonequilibrium phonons.