  The $\gamma$-ray emission from stars is induced by the interaction of cosmic
rays with stellar atmospheres and photon fields. This emission is expected to
come in two components: a stellar disk emission, where $\gamma$-rays are mainly
produced in atmospheric showers generated by hadronic cosmic rays, and an
extended halo emission, where the high density of soft photons in the
surroundings of stars create a suitable environment for $\gamma$-ray production
via inverse Compton (IC) scattering by cosmic-ray electrons. Besides the Sun,
no other disk or halo from single stars has ever been detected in
$\gamma$-rays. However, by assuming a cosmic-ray spectrum similar to that
observed on Earth, the predicted $\gamma$-ray emission of super-luminous stars,
like e.g. Betelgeuse and Rigel, could be high enough to be detected by the
Fermi Large Area Telescope (LAT) after its first decade of operations. In this
work, we use 12 years of Fermi-LAT observations along with IC models to study 9
super-luminous nearby stars, both individually and via stacking analysis. Our
results show no significant $\gamma$-ray emission, but allow us to restrict the
stellar $\gamma$-ray fluxes to be on average $<3.3 \times 10^{-11}$ ph
cm$^{-2}$ s$^{-1}$ at a 3$\sigma$ confidence level, which translates to an
average local density of electrons in the surroundings of our targets to be
less than twice of that observed for the Solar System.
