Context. Models of the escape and retention of volatiles by minor icy objects exclude any presence of volatile ices on the surface of trans-Neptunian objects (TNOs) smaller than ~1000 km in diameter at the typical temperature in this region of the solar system, whereas the same models show that water ice is stable on the surface of objects over a wide range of diameters. Collisions and cometary activity have been used to explain the process of surface refreshing of TNOs and Centaurs. These processes can produce surface heterogeneity that can be studied by collecting information at different rotational phases. Aims: The aims of this work are to study the surface composition of (20000) Varuna, a TNO with a diameter 668+154-86 km and to search for indications of rotational variability. Methods: We observed (20000) Varuna during two consecutive nights in January 2011 with the near-infrared camera and spectrometer NICS at the Telescopio Nazionale Galileo, La Palma, Spain. We used the low resolution mode with the AMICI prism to obtain a set of spectra covering the whole rotation period of the Varuna (Pr = 6.34 h). We fit the resulting relative reflectance with radiative transfer models of the surface of atmosphereless bodies. Results: After studying the spectra corresponding to different rotational phases of Varuna, we did not find any indication of surface variability at 2σ level. In all the spectra, we detect an absorption at 2.0 μm, suggesting the presence of water ice on the surface. We do not detect any other volatiles on the surface, although the signal-to-noise ratio is not high enough to discard their presence in small quantities. Based on scattering models, we present two possible compositions compatible with our set of data and discuss their implications in the framework of the collisional history of the trans-Neptunian belt. Conclusions: We find that the most probable composition for the surface of Varuna is a mixture of amorphous silicates, complex organics, and water ice. This composition is compatible with all the materials being primordial, so no replenishment mechanism is needed in the equation. However, our data can also be fitted by models containing up to a 10% of methane ice. For an object with the characteristics of Varuna, this volatile could not be primordial, so an event, such as an energetic impact, would be needed to explain its presence on the surface.