  Interacting dark matter (DM) - dark energy (DE) models have been intensively
investigated in the literature for their ability to fit various data sets as
well as to explain some observational tensions persisting within the
$\Lambda$CDM cosmology. In this work, we employ Gaussian processes (GP)
algorithm to perform a joint analysis by using the geometrical cosmological
probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic
Oscillations and the H0LiCOW lenses sample to infer a reconstruction of the
coupling function between the dark components in a general framework, where the
DE can assume a dynamical character via its equation of state. In addition to
the joint analysis with these data, we simulate a catalog with standard siren
events from binary neutron star mergers, within the sensitivity predicted by
the Einstein Telescope, to reconstruct the dark sector coupling with more
accuracy in a robust way. We find that the particular case, where $w = -1$ is
fixed on the DE nature, has a statistical preference for an interaction in the
dark sector at late times. In the general case, where $w(z)$ is analyzed, we
find no evidence for such dark coupling, and the predictions are compatible
with the $\Lambda$CDM paradigm. When the mock events of the standard sirens are
considered to improve the kernel in GP predictions, we find preference for an
interaction in the dark sector at late times.
