We present novel nonparametric representation math for local pseudopotentials (PP) based on Gaussian Process Regression (GPR). Local pseudopotentials are needed for materials simulations using Orbital-Free Density Functional Theory (OF-DFT) to reduce computational cost and to allow kinetic energy functional (KEF application only to the valence density. Moreover, local PPs are important for the development of accurate KEFs for OF-DFT, but they are only available for a limited number of elements. We optimize local PPs of tin (Sn) represented with GPR to reproduce the experimental lattice constants of alpha- and beta-Sn and the energy difference between these two phases as well as their electronic structure and charge density distributions which are obtained with Kohn-Sham Density Functional Theory employing semilocal PPs. The use of a nonparametric GPR-based PP representation avoids difficulties associated with the use of parametrized functions and has the potential to construct an optimal local PP independent of prior assumptions. The GPR-based Sn local PP results in well-reproduced bulk properties of alpha- and beta-tin and electronic valence densities similar to those obtained with semilocal PP.