  We present an analysis of the sensitivity of current and future LHC searches
for new spin-0 particles in top-anti-top-quark ($t\bar{t}$) final states,
focusing on generic axion-like particles (ALPs) that are coupled to top quarks
and gluons. As a first step, we derive new limits on the effective ALP
Lagrangian in terms of the Wilson coefficients $c_t$ and $c_{\tilde{G}}$ based
on the results of the CMS search using $35.9$ fb$^{-1}$ of data, collected at
$\sqrt{s} = 13$ TeV. We then investigate how the production of an ALP with
generic couplings to gluons and top quarks can be distinguished from the
production of a pseudoscalar which couples to gluons exclusively via a
top-quark loop. To this end, we make use of the invariant $t\bar{t}$ mass
distribution and angular correlations that are sensitive to the $t\bar{t}$ spin
correlation. Using a mass of 400 GeV as an example, we find that already the
data collected during Run 2 and Run 3 of the LHC provides an interesting
sensitivity to the underlying nature of a possible new particle. We also
analyze the prospects for data anticipated to be collected during the
high-luminosity phase of the LHC. Finally, we compare the limits obtained from
the $t \bar t$ searches to existing experimental bounds from LHC searches for
narrow di-photon resonances, from measurements of the production of four top
quarks, and from global analyses of ALP-SMEFT interference effects.
