  Using data from the \emph{Fermi} Large Area Telescope we perform a detailed
study of the GeV emission in the direction of G51.26+0.09 to constrain its
origin, its possible relation to this SNR, the star-forming region
G051.010+00.060 seen nearby in the sky, or the pulsars known in the region, and
to derive the properties of the underlying cosmic ray particles producing the
non-thermal radiation. We also study properties of the environment which could
shed light on the nature of the source of the gamma rays. We compare the
morphology of the gamma-ray radiation to that of the emission detected at radio
wavelengths in previous observations. Modeling the measured spectrum and fluxes
of the high-energy radiation allows us to derive the properties of the particle
populations that could produce this emission in several possible scenarios. We
use existing data from $^{13}$CO emission and neutral hydrogen emission to
probe the environment, searching for possible morphological features associated
to the gamma rays and SNR. We rule out the star-forming region G051.010+00.060
as the origin of the GeV emission. The correspondence seen between the
gamma-ray and radio morphologies support an SNR scenario, where the object
responsible is more extended than G51.26+0.09, or is made up of more than one
unresolved SNR. Given the flat spectral energy distribution observed at GeV
energies and the radio flux upper limits, we also rule out bremsstrahlung
emission as the origin of the gamma rays. A pulsar wind nebula origin of the
high-energy photons, associated to the pulsar PSR J1926+1613, cannot be ruled
out or confirmed, due to its unknown parameters such as spin-down power and
age, while the pulsars PSR J1924+1628 and PSR J1924+1631 are too far away to be
the source of gamma rays.
