  The three major large-scale, diffuse $\gamma$-ray structures of the Milky Way
are the Galactic disk, a bulge-like GeV excess towards the Galactic center, and
the Fermi bubble. Whether such structures can also be present in other normal
galaxies remains an open question. M31, as the nearest massive normal galaxy,
holds promise for spatially-resolving the $\gamma$-ray emission. Based on more
than 8 years of Fermi-LAT observations, we use (1) disk, (2) bulge, and (3)
disk-plus-bulge templates to model the spatial distribution of the $\gamma$-ray
emission from M31. Among these, the disk-plus-bulge template delivers the
best-fit, in which the bulge component has a TS value 25.7 and a photon-index
of $2.57\pm0.17$, providing strong evidence for a centrally-concentrated
gamma-ray emission from M31, that is analogous to the Galactic center excess.
The total 0.2-300 GeV gamma-ray luminosity from this bulge component is
$(1.16\pm0.14)\times10^{38} erg s^{-1}$, which would require
$\sim1.5\times10^5$ millisecond pulsars, if they were the dominant source. We
also search for a Fermi bubble-like structure in M31 using the full dataset
(pass8), but no significant evidence is found. In addition, a likelihood
analysis using only photons with the most accurate reconstructed direction
(i.e., PSF3-only data) reveals a 4.8 $\sigma$ point-like source located at
$\sim$ 10kpc to the northwest of the M31 disk, with a luminosity of
$(0.97\pm0.27)\times10^{38} erg s^{-1}$ and a photon-index of $2.31\pm0.18$.
Lacking of a counterpart on the southeast side of the disk, the relation
between this point-like source and a bubble-like structure remains elusive.
