The atmospheric antiproton flux resulting from $pp \rightarrow ppp \bar{p}$-type interactions has been measured by BESS\,\cite{pbar_atmos}. Here, the feasibility of measuring the equivalent atmospheric antineutron flux through the annihilation charged-residues is investigated. The proposed detection technique is based on the use of a $250 l$ liquid scintillator cylindrical volume surrounded by eight plastic scintillator plates, used for triggering. The potential interest of this measurements is associated to the current experimental effort to observe neutron-antineutron oscillations \cite{nnbarreview}, where atmospheric antineutrons could represent a background.