We investigate the possibility to explain theoretically the S2 star orbital precession around the massive object at the Galactic Centre using Extended Theories of Gravity [1], specifically f(R, φ) a Sanders-like [2] 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 the 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 [3,4] seems reliable to constrain modified gravity models at astronomical level.17th National Conference of Astronomers of Serbia : Book of abstracts; September 23-27,2014, Belgrad