We propose the design of all-dielectric isotropic micro-or nanoparticles which, when used as structural elements of a metamaterial, can simultaneously provide negative effective electric permittivity and negative magnetic permeability. The particles comprise three dielectric layers with specially adjusted parameters, which ensure simultaneous excitation of the electric and magnetic Mie dipole modes. The layer parameters were found by the Mie scattering analysis and then verified by the simulations, which confirmed the double-negative behavior of the metamaterial at up to visible light frequencies. The isotropy of such particles suggests the possibility of using them in a double-negative liquid metamaterial.