Context. Near-Earth asteroid (175706) 1996 FG3 is the primary target of the ESA Marco Polo-R mission, which was selected for the assessment study phase of ESA M3 missions. This is a primitive (C-type), binary asteroid that will allow new research to be performed. The primary is a rapidly rotating (3.6 h) small asteroid (1.4 km diameter) that is almost spherical and has a satellite of ~400 m. Aims: We analyse new ground-based spectroscopic data of 1996 FG3 to help us characterise its surface composition and prepare for the mission. Methods: We obtained a near-infrared spectrum covering the range 0.8-2.5 μm, using the camera-spectrograph NICS at the 3.6 m telescope TNG (Telescopio Nazionale Galileo), located at "El Roque de los Muchachos" Observatory on La Palma, Spain. We combine our near-infrared spectrum with previously published data, and compare all the available spectra of this asteroid with the spectra of meteorites to constrain the mineralogy of the asteroid. Results: Our spectrum of FG3 differs remarkably from previously published ones. Spectral classification performed using the complete visible and near-infrared range yields more than one result, varying from C to Xk types. However, all the possible spectral types indicate that this asteroid is a primitive object. The comparison with meteorites behaves in the same way, providing several good matches to our new near-infrared spectrum (CM2 carbonaceous chondrite, and L6 and H4 ordinary chondrites), and only one match in the case of the previously published spectra (weakly shocked H4 ordinary chondrite, dark vein). The albedo of the asteroid (~0.04), is typical of a primitive object, and is consistent with the reflectance value at 0.55 μm of the CM2 carbonaceous chondrite. Further observations will be essential to help us characterise more clearly the mineralogy of this asteroid.