  An excess of $\gamma$-ray emission from the Galactic Center (GC) region with
respect to predictions based on a variety of interstellar emission models and
$\gamma$-ray source catalogs has been found by many groups using data from the
{\it Fermi} Large Area Telescope (LAT). Several interpretations of this excess
have been invoked. In this paper we search for members of an unresolved
population of $\gamma$-ray pulsars located in the inner Galaxy that are
predicted by the interpretation of the GC excess as being due to a population
of such sources. We use cataloged LAT sources to derive criteria that
efficiently select pulsars with very small contamination from blazars. We
search for point sources in the inner $40^\circ\times40^\circ$ region of the
Galaxy, derive a list of approximately 400 sources, and apply pulsar selection
criteria to extract pulsar candidates among our source list. We performed the
entire data analysis chain with two different interstellar emission models
(IEMs), and found a total of 135 pulsar candidates, of which 66 were selected
with both IEMs.
