Context. Near-Earth binary asteroid (175706) 1996 FG3 is the current backup target of the ESA MarcoPolo-R mission, selected for the study phase of ESA M3 missions. It is a primitive (C-type) asteroid that shows significant variation in its visible and near-infrared spectra. Aims: Here we present new visible and near-infrared spectra of 1996 FG3. We compare our new data with other published spectra, analysing the variation in the spectral slope. The asteroid will not be observable again over the next three years at least. Methods: We obtained visible and near-infrared spectra using DOLORES and NICS instruments, respectively, at the Telescopio Nazionale Galileo (TNG), a 3.6 m telescope located at El Roque de los Muchachos Observatory in La Palma, Spain. To compare with other published spectra of the asteroid, we computed the spectral slope S', and studied any plausible correlation of this quantity with the phase angle (α). Results: In the case of visible spectra, we find a variation in spectral slope of ΔS' = 0.15 ± 0.10%/103 Å/° for 3°<α< 18°, which is in good agreement with the values found in the literature for the phase reddening effect. In the case of the near-infrared, there seems to be a trend between the reddening of the spectra and the phase angle, excluding one point. We find a variation in the slope of ΔS' = 0.04 ± 0.08%/103 Å/° for 6° <α < 51°. Our computed variation in S' is in good agreement with the only two values found in the literature for the phase reddening in the near-infrared. Conclusions: The variation in the spectral slope of asteroid 1996 FG3 shows a trend with the phase angle at the time of the observations, both in the visible and the near-infrared. It is worth noting that, to fully explain this spectral variability we should take into account other factors, like the position of the secondary component of the binary asteroid 1999 FG3 with respect to the primary, or the spin axis orientation at the time of the observations. More data are necessary for an analysis of this kind.