  One of the novelties of the Gaia-DR3 with respect to the previous data
releases is the publication of the multiband light curves of about 1 million
AGN. The goal of this work was the creation of a catalogue of variable AGN,
whose selection was based on Gaia data only. We first present the
implementation of the methods to estimate the variability parameters into a
specific object study module for AGN. Then we describe the selection procedure
that led to the definition of the high-purity variable AGN sample and analyse
the properties of the selected sources. We started from a sample of millions of
sources, which were identified as AGN candidates by 11 different classifiers
based on variability processing. Because the focus was on the variability
properties, we first defined some pre-requisites in terms of number of data
points and mandatory variability parameters. Then a series of filters was
applied using only Gaia data and the Gaia Celestial Reference Frame 3
(Gaia-CRF3) sample as a reference.The resulting Gaia AGN variable sample, named
GLEAN, contains about 872000 objects, more than 21000 of which are new
identifications. We checked the presence of contaminants by cross-matching the
selected sources with a variety of galaxies and stellar catalogues. The
completeness of GLEAN with respect to the variable AGN in the last Sloan
Digital Sky Survey quasar catalogue is about 47%, while that based on the
variable AGN of the Gaia-CRF3 sample is around 51%. From both a comparison with
other AGN catalogues and an investigation of possible contaminants, we conclude
that purity can be expected to be above 95%. Multiwavelength properties of
these sources are investigated. In particular, we estimate that about 4% of
them are radio-loud. We finally explore the possibility to evaluate the time
lags between the flux variations of the multiple images of strongly lensed
quasars, and show one case.
