  Despite the increasing number of Gravitational Wave (GW) detections, the
astrophysical origin of Binary Black Hole (BBH) mergers remains elusive. A
promising formation channel for BBHs is inside accretion discs around
supermassive black holes, that power Active Galactic Nuclei (AGN). In this
paper, we test for the first time the spatial correlation between observed GW
events and AGN. To this end, we assemble all sky catalogues with 1,412 (242)
AGN with a bolometric luminosity greater than $10^{45.5} {\rm erg\ s}^{-1}$
($10^{46}\,{\rm erg\,s}^{-1}$) with spectroscopic redshift of $z\leq0.3$ from
the Milliquas catalogue, version 7.7b. These AGN are cross-matched with
localisation volumes of BBH mergers observed in the same redshift range by the
LIGO and Virgo interferometers during their first three observing runs. We find
that the fraction of the detected mergers originated in AGN brighter than
$10^{45.5}\,{\rm erg\,s}^{-1}$ ($10^{46}\,{\rm erg\,s}^{-1}$) cannot be higher
than $0.49$ ($0.17$) at a 95 per cent credibility level. Our upper limits imply
a limited BBH merger production efficiency of the brightest AGN, while most or
all GW events may still come from lower luminosity ones. Alternatively, the AGN
formation path for merging stellar-mass BBHs may be actually overall
subdominant in the local Universe. To our knowledge, ours are the first
observational constraints on the fractional contribution of the AGN channel to
the observed BBH mergers.
