  The topological susceptibility, $\chi^4$, following the work of Witten and
Veneziano, plays a key role in identifying the relative magnitude of the
$\eta^{\prime}$ mass, the so-called $U(1)_{A}$ problem. A nonzero $\chi^4$ is
caused by the Veneziano ghost, the occurrence of an unphysical massless pole in
the correlation function of the topological current. In a recent paper
(Phys.Rev.Lett.114 (2015) 24, 242001), an explicit relationship between this
Veneziano ghost and color confinement was proposed, by connecting the dynamics
of the Veneziano ghost, and thus the topological susceptibility, with Gribov
copies. However, the analysis is incompatible with BRST symmetry (Phys.Rev.D 93
(2016) no.8, 085010). In this paper, we investigate the topological
susceptibility, $\chi^4$, in SU(3) and SU(2) Euclidean Yang-Mills theory using
an appropriate Pad\'e approximation tool and a non-perturbative gluon
propagator, within a BRST invariant framework and by taking into account Gribov
copies in a general linear covariant gauge.
