  The presence of massive black holes (BHs) with masses of order $10^9\rm\,
M_\odot$, powering bright quasars when the Universe was less than 1 Gyr old,
poses strong constraints on their formation mechanism. Several scenarios have
been proposed to date to explain massive BH formation, from the low-mass seed
BH remnants of the first generation of stars to the massive seed BHs resulting
from the rapid collapse of massive gas clouds. However, the plausibility of
some of these scenarios to occur within the progenitors of high-z quasars has
not yet been thoroughly explored. In this work, we investigate, by combining
dark-matter only N-body simulations with a semi-analytic framework, whether the
conditions for the formation of massive seed BHs from synchronised
atomic-cooling halo pairs and/or dynamically-heated mini-haloes are fulfilled
in the overdense regions where the progenitors of a typical high-redshift
quasar host form and evolve. Our analysis shows that the peculiar conditions in
such regions, i.e. strong halo clustering and high star formation rates, are
crucial to produce a non-negligible number of massive seed BH host candidates:
we find $\approx1400$ dynamically heated metal-free mini-haloes, including one
of these which evolves to a synchronised pair and ends up in the massive
quasar-host halo by $z=6$. This demonstrates that the progenitors of
high-redshift quasar host haloes can harbour early massive seed BHs. Our
results further suggest that multiple massive seed BHs may form in or near the
quasar host's progenitors, potentially merging at lower redshifts and yielding
gravitational wave events.
