The Andromeda galaxy is the closest spiral galaxy to us and has been the subject of numerous studies. It harbors a massive dark matter halo, which may span up to ~600 kpc across and comprises ~90% of the galaxy's total mass. This halo size translates into a large diameter of 42° on the sky, for an M31-Milky Way (MW) distance of 785 kpc, but its presumably low surface brightness makes it challenging to detect with γ-ray telescopes. Using 7.6 yr of Fermi Large Area Telescope (Fermi-LAT) observations, we make a detailed study of the γ-ray emission between 1-100 GeV toward M31's outer halo, with a total field radius of 60° centered at M31, and perform an in-depth analysis of the systematic uncertainties related to the observations. We use the cosmic-ray propagation code GALPROP to construct specialized interstellar emission models to characterize the foreground γ-ray emission from the MW, including a self-consistent determination of the isotropic component. We find evidence for an extended excess that appears to be distinct from the conventional MW foreground, having a total radial extension upward of ~120-200 kpc from the center of M31. We discuss plausible interpretations of the excess emission, but emphasize that uncertainties in the MW foreground-and in particular, modeling of the H i-related components-have not been fully explored and may impact the results.