We introduce a Finslerian model related to the classical Garner dynamical system, which models the cancer cell population growth. The Finsler structure is determined by the energy of the deformation field--the difference of the fields, which describe the reduced and the proper biological models. It is shown that a certain locally-Minkowski anisotropic Randers structure, obtained by means of statistical fitting, is able to provide a Zermelo-type drift of the overall cancer cell population growth, which occurs due to significant changes within the cancerous process. The geometric background, the applicative advantages and perspective openings of the constructed geometric structure are discussed.