To construct a dielectric analog of a spaser, we study several configurations of cluster-based unit cells for an all-dielectric metasurface characterized by resonant conditions of the trapped mode excitation. Excitation of the trapped mode is realized by performing either specific displacement of particles in the cluster or perturbation of the equidistantly spaced particles by off-centered holes. The latter approach is more advantageous for enhancement of the electric near-field with homogeneous distribution in-plane of the structure and strong field localization outside the high-refractive-index dielectric particles. This feature opens prospects for realization of subwavelength flat lasing structures based on strong near-field interaction with substances exhibiting nonlinear characteristics and properties of gain media.