  We present a systematic study of the correlators used experimentally to probe
the Chiral Magnetic Effect (CME) using the Anomalous Viscous Fluid Dynamics
(AVFD) model in Pb--Pb and Xe--Xe collisions at LHC energies. We find a
parametrization that describes the dependence of these correlators on the value
of the axial current density ($n_5/\mathrm{s}$), which dictates the CME signal,
and on the parameter that governs the background in these measurements i.e.,
the percentage of local charge conservation (LCC) within an event. This allows
to deduce the values of $n_5/\mathrm{s}$ and the LCC percentage that provide a
quantitative description of the centrality dependence of the experimental
measurements. We find that the results in Xe--Xe collisions at
$\sqrt{s_{\mathrm{NN}}} = 5.44$~TeV are consistent with a background only
scenario. On the other hand, the model needs a significant non-zero value of
$n_5/\mathrm{s}$ to match the measurements in Pb--Pb collisions at
$\sqrt{s_{\mathrm{NN}}} = 5.02$~TeV.
