We investigate the possibility to explain theoretically the S2 star orbital precession around the massive object at Galactic Centre using Extended Theories of Gravity, specifically f(R, φ) a Sanders-like gravitational potential in total absence of dark matter. To this aim an analytic fourth-order theory of gravity, non-minimally coupled with a massive scalar field is considered. The interaction term is given by an analytic functions f(R, φ) where R is the Ricci scalar and φ is the scalar field. We simulated orbit of S2 star around Galactic Centre in Sanders-like gravity potentials and compared it with NTT/VLT observations. We presented maps of reduced χ 2 over the {α − mφ} parameter space in the case of NTT/VLT observations. The approach we are proposing seems reliable to constrain modified gravity models at astronomical level