Quiescent emission from the neutron star low-mass X-ray binary Cen X-4 is seen to be variable on time-scales from hundreds of seconds to years, suggesting that at least in this object, low-level accretion is important during quiescence. Here, we present results from recent XMM–Newton and Swift observations of Cen X-4, where the X-ray flux (0.5–10 keV) varies by a factor of 6.5 between the brightest and faintest states. We find a positive correlation between the X-ray flux and the simultaneous near-ultraviolet (UV) flux, where as there is no significant correlation between the X-ray and simultaneous optical (V, B) fluxes. This suggests that while the X-ray and UV emitting regions are somehow linked, the optical region originates elsewhere. Comparing the luminosities, it is plausible that the UV emission originates due to reprocessing of the X-ray flux by the accretion disc, with the hot inner region of the disc being a possible location for the UV emitting region. The optical emission, however, could be dominated by the donor star. The X-ray/UV correlation does not favour the accretion stream impact point as the source of the UV emission.