  Context. The study of the oldest and most metal-poor stars in our Galaxy
promotes our understanding of the Galactic chemical evolution and the beginning
of Galaxy and star formation. However, they are notoriously difficult to find,
with only five stars at $\mathrm{[Fe/H]<-5.0}$ having been detected to date.
Thus, the spectrophotometric data of 219 million sources which became available
in the third Gaia Data Release comprise a very promising dataset for the
identification of metal-poor stars. Aims. We want to use the low-resolution
Gaia Blue Photometer / Red Photometer (BP/RP) spectra to identify metal-poor
stars. Our primary aspiration is to help populate the poorly constrained tail
of the metallicity distribution function of the stellar halo of the Galaxy.
Methods. We developed a metal-poor candidate selection method based on flux
ratios from the BP/RP Gaia spectra, using simulated synthetic spectra. Results.
We found a relation between the relative iron abundance and the flux ratio of
the Ca H \& K region to that of the $\mathrm{H\beta}$ line. This relation is
temperature and surface gravity dependent, and it holds for stars with
$\mathrm{4800\,K \leq T_{eff}\leq6300\,K}$. We applied it to noisy simulated
synthetic spectra and inferred $\mathrm{[Fe/H]}$ with an uncertainty of
$\sigma_{\mathrm{[Fe/H]}}\lessapprox0.65$ dex for $\mathrm{-3\leq[Fe/H]}\leq
0.5$ and G=15-17mag, which is sufficient to identify stars at
$\mathrm{[Fe/H]<-2.0 }$ reliably. We predict that by selecting stars with
inferred $\mathrm{[Fe/H]}\leq-2.5$ dex, we can retrieve 80% of the stars with
$\mathrm{[Fe/H]}\leq-3$ and have a success rate of about 50%, that is one in
two stars we select would have $\mathrm{[Fe/H]}\leq-3$. We do not take into
account the effect of reddening, so our method should only be applied to stars
which are located in regions of low extinction.
