  HESS J1614$-$518 and HESS J1616$-$508 are two tera-electron volt (TeV)
$\gamma$-ray sources that are not firmly associated with any known counterparts
at other wavelengths. We investigate the distribution of interstellar medium
towards the TeV $\gamma$-ray sources using results from a 7 mm-wavelength Mopra
study, the Mopra Southern Galactic Plane CO Survey, the Millimetre Astronomer's
Legacy Team - 45 GHz survey and [CI] data from the HEAT telescope. Data in the
CO(1$-$0) transition lines reveal diffuse gas overlapping the two TeV sources
at several velocities along the line of sight, while observations in the
CS(1$-$0) transition line reveal several interesting dense gas features. To
account for the diffuse atomic gas, archival HI data was taken from the
Southern Galactic Plane Survey. The observations reveal gas components with
masses $\sim10^3$ to $10^5$ M$_\odot$ and with densities $\sim10^2$ to $10^3$
cm$^{-3}$ overlapping the two TeV sources. Several origin scenarios potentially
associated with the TeV $\gamma$-ray sources are discussed in light of the
distribution of the local interstellar medium. We find no strong convincing
evidence linking any counterpart with HESS J1614$-$518 or HESS J1616$-$508.
