We study Modified Gravity (MG) theories by modelling the redshifted matter power spectrum in a spherical Fourier–Bessel basis. We use a fully non-linear description of the real-space matter power spectrum and include the lowest order redshift-space correction (Kaiser effect), taking into account some additional non-linear contributions. Ignoring relativistic corrections, which are not expected to play an important role for a shallow survey, we analyse two different MG scenarios, namely the generalized Dilaton scalar–tensor theories and the f (R) models in the large curvature regime. We compute the 3D power spectrum Csℓ(k1,k2) for various such MG theories with and without redshift-space distortions, assuming precise knowledge of background cosmological parameters. Using an all-sky spectroscopic survey with Gaussian selection function φ(r)∝exp(−r2/r20),r0=150h−1Mpc, and number density of galaxies N¯=10−4Mpc−3⁠, we use a χ2 analysis, and find that the lower order (ℓ ≤ 25) multipoles of Csℓ(k,k′) (with radial modes restricted to k < 0.2 h Mpc−1) can constraint the parameter fR0 at a level of 2 × 10−5(3 × 10−5) with 3σ confidence for n = 1(2). Combining constraints from higher ℓ > 25 modes can further reduce the error bars and thus in principle make cosmological gravity constraints competitive with Solar system tests. However this will require an accurate modelling of non-linear redshift-space distortions. Using a tomographic β(a)–m(a) parametrization we also derive constraints on specific parameters describing the Dilaton models of MG.