Elasticity image, visualizing the quantitative map of tissue stiffness, can be reconstructed by solving an inverse problem. Classical methods for magnetic resonance elastography (MRE) try to solve a regularized optimization problem comprising a deterministic physical model and a prior constraint as data-fidelity term and regularization term, respectively. For improving the elasticity reconstructions, appropriate prior about the underlying elasticity distribution is required which is not unique. This article proposes an infused approach for MRE reconstruction by integrating the statistical representation of the physical laws of harmonic motions and learning-based prior. For data-fidelity term, we use a statistical linear-algebraic model of equilibrium equations and for the regularizer, data-driven regularization by denoising (RED) is utilized. In the proposed optimization paradigm, the regularizer gradient is simply replaced by the residual of learned denoiser leading to time-efficient computation and convex explicit objective function. Simulation results of elasticity reconstruction verify the effectiveness of the proposed approach.