  The prototypical powerful FR \Romannum{2} radio galaxy Cygnus A fits
extremely well into the quasar/radio galaxy unified model: high polarization
with an angle almost perpendicular to the radio jet and polarized flux showing
broad permitted lines. It has been claimed that ionized gas in the torus
reveals a very clear torus shape via Bremmstrahlung emission. We rule out the
later with an energetic argument, and we constrain the molecular and atomic gas
properties with existing observations. The atomic absorption against the core
has been shown to match the X-ray column only if the spin temperature is an
implausible $T_{\rm s} = 1\times 10^6$ K. This points to a molecular medium for
the X-ray column $\log(N_{\rm H} ~[\rm{cm^{-2}}]) \sim 23.5$. Yet not low-J CO
absorption is detected to sensitive limits. The non-detection is surprising
given that this powerful radio galaxy hosts a luminous, dust-obscured active
nucleus and copious warm molecular hydrogen. These conditions suggest a
detectable level of emission. Furthermore, the torus X-ray column density
suggests detectable absorption. We explore various possibilities to explain the
lack of a signature from warm CO (200-250K). Specifically, that the radiative
excitation by the radio core renders low-J CO absorption below current
sensitivities, and that high-J levels are well populated and conducive to
producing absorption. We test this hypothesis using archival
\textit{Hershel}/SPIRE FTS observations of Cygnus A of high-J CO lines ($14
\geq J \geq 4$ transitions). Still high-J CO lines are not detected. We suggest
that ALMA observations near its high frequency limit can be critical to obtain
the signature of molecular line of the torus of Cygnus A.
