HESS J1614–518 and HESS J1616–508 are two tera-electron volt γ-ray sources that are not firmly associated with any known counterparts at other wavelengths. We investigate the distribution of interstellar medium towards the tera-electron volt γ-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 [C i] data from the HEAT telescope. Data in the CO(1–0) transition lines reveal diffuse gas overlapping the two tera-electron volt 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 H i data was taken from the Southern Galactic Plane Survey. The observations reveal gas components with masses ~103 to 105 M⊙ and with densities ~102 to 103 cm−3 overlapping the two tera-electron volt sources. Several origin scenarios potentially associated with the tera-electron volt γ-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.