Candidate quasars for 4MOST–Gaia PAQS are selected based purely on the fact that quasars are stationary sources on the sky (Heintz et al. 2018). We select sources from the Gaia catalog with proper motions and parallaxes consistent with zero at the 2-σ level down to a limit of G < 20.5 mag. The completeness of our survey is therefore limited only by the fibre allocation efficiency (up to ~80%). However, since the fibre allocation does not depend on the colour of the targets, this lower completeness will not introduce any selection bias. Since the number of stationary sources in the Gaia catalog increases drastically when observing close to the Galactic plane, we have limited our survey area to high Galactic latitudes, b < –60 deg. Based on a pilot study carried out at the North Galactic Pole (Heintz et al. 2020), we have estimated the stellar contamination to be around 40% over the entire survey area. In total, 4G-PAQS will obtain a colour-unbiased sample of ~100,000 quasars with no prior selection on redshift nor spectral shape.