Light-to-heat conversion that occurs when irradiating a metal nanoparticle within a polymer matrix with ultrashort laser pulses initiates photothermal destruction of dissolved precursor molecules just near the nanoparticle. Extracted elementary species deposit on the nanoparticle surface, forming a core-shell structure. We construct an approximate analytical model for this process. The necessary step here is the diffusion of the precursor molecules towards the nanoparticle surface, replacing the broken ones. This diffusion can be a limiting factor for the rate of the shell growth. However, we show that because of the sharp localization of the process the precursor diffusion can successfully supply the growing shell with elementary species at realistic values of the precursor diffusion coefficient if the sample is kept in viscoelastic state at a temperature near the glass transition between the laser pulses. The main restriction on the obtained shell thickness comes from the requirement of matrix stability during the laser processing. Taking this restriction into account, the model allows estimating reachable shell thicknesses depending on the kinetic parameters of the precursor destruction reaction. This paper relies on numerous publications on photo/laser-induced growth of homogeneous metal or semiconductor nanoparticles within polymer matrices; however, this type of growth for compound core-shell nanoparticles is studied for the first time, to our knowledge.