  We suggest a simplified model that simultaneously addresses the dark-matter
problem and give rise to top quark flavor changing neutral current (FCNC)
interactions at the one-loop order. The model consists of two extra $SU(2)_L$
gauge singlets: a colored mediator of spin zero ($S$) and a right-handed
fermion ($\chi$) both are odd under an ad-hoc $Z_2$ symmetry. The right-handed
fermion plays the role of the dark-matter candidate. In this model, the
presence of the two dark sector particles generates one-loop induced FCNC
decays of the top quark into light quarks and bosons such as the gluon, the
photon, the $Z$-boson or the Higgs boson. As a case study, we analyze the top
quark FCNC decays into light quarks ($u$ or $c$) and a $Z$ or Higgs bosons. We
then study the reliable solutions to the dark-matter problem by estimating the
regions in the parameter space that are consistent with the \textsc{Planck}
measurement of the dark-matter relic density. We also revisit the bounds from
the searches of dark matter in events with at least one high-$p_T$ jet and
large missing transverse energy at the Large Hadron Collider (LHC). We then
define four benchmark points that are consistent with the existing constraints
from collider experiments and cosmology. We finally estimate, for these
benchmark scenarios, the rates of a broad range of channels that can be used to
probe the connection between the top FCNC transitions and dark matter both at
the HL-LHC and a future $100$ TeV collider.
