  Colliding-wind binaries (CWBs) constitute an emerging class of $\gamma$-ray
sources powered by strong, dense winds in massive stellar systems. The most
powerful of them are those binaries hosting a Wolf-Rayet (WR) star. Following
the recent discovery of Apep -- the closest known Galactic WR--WR binary -- we
discuss the non-detection of its putative high-energy emission by the Fermi
Large Area Telescope (Fermi-LAT) in this Letter. The limits reported in the GeV
regime can be used to set a lower limit on the magnetic field pressure density
within the shocked wind-collision region (WCR), and to exclude Apep as a bright
gamma-ray emitting binary. Given that this WR--WR system is the most luminous
CWB identified until now at radio wavelengths, this result proves unambiguously
that non-thermal synchrotron emission is not a suitable identifier for the
subset of gamma-ray emitters in this class of particle accelerators. Rather,
Apep could be an interesting case of study for magnetic field amplification in
shocked stellar winds.
