Context. Extreme ultraviolet (EUV) observations of the quiet solar atmosphere reveal extended regions of weak emission compared to the ambient quiescent corona. The magnetic nature of these coronal features is not well understood. Aims. We study the magnetic properties of the weakly emitting extended regions, which we name coronal voids. In particular, we aim to understand whether these voids result from a reduced heat input into the corona or if they are associated with mainly unipolar and possibly open magnetic fields, similar to coronal holes. Methods. We defined the coronal voids via an intensity threshold of 75% of the mean quiet-Sun (QS) EUV intensity observed by the high-resolution EUV channel (HRIEUV) of the Extreme Ultraviolet Imager on Solar Orbiter. The line-of-sight magnetograms of the same solar region recorded by the High Resolution Telescope of the Polarimetric and Helioseismic Imager allowed us to compare the photospheric magnetic field beneath the coronal voids with that in other parts of the QS. Results. The coronal voids studied here range in size from a few granules to a few supergranules and on average exhibit a reduced intensity of 67% of the mean value of the entire field of view. The magnetic flux density in the photosphere below the voids is 76% (or more) lower than in the surrounding QS. Specifically, the coronal voids show much weaker or no network structures. The detected flux imbalances fall in the range of imbalances found in QS areas of the same size. Conclusions. We conclude that coronal voids form because of locally reduced heating of the corona due to reduced magnetic flux density in the photosphere. This makes them a distinct class of (dark) structure, different from coronal holes.