  We applied image stacking on empty-field Faint Images of the Radio Sky at
Twenty-Centimeters (FIRST) survey maps centred on optically identified
high-redshift quasars at $z\geq4$ to uncover the hidden $\mu$Jy radio emission
in these active galactic nuclei (AGN). The median stacking procedure for the
full sample of $2229$ optically identified AGN uncovered an unresolved point
source with an integrated flux density of 52$~\mu$Jy, with a signal-to-noise
ratio $\sim10$. We co-added the individual image centre pixels to estimate the
characteristic monochromatic radio power at $1.4~$GHz considering various
values for the radio spectral index, revealing a radio population with
$P_\mathrm{1.4GHz}\sim10^{24}~$W Hz$^{-1}$. Assuming that the entire radio
emission originates from star-forming (SF) activity in the nuclear region of
the host galaxy, we obtained an upper limit on the characteristic star
formation rate, $\sim4200~$M$_\odot~$yr$^{-1}$. The angular resolution of FIRST
images is insufficient to distinguish between the SF and AGN origin of radio
emission at these redshifts. However, a comparison with properties of
individual sources from the literature indicates that a mixed nature is likely.
Future very long baseline interferometry radio observations and ultra-deep
Square Kilometre Array surveys are expected to be sensitive enough to detect
and resolve the central $1-10~$kpc region in the host galaxies, and thus
discriminate between SF and AGN related emission.
