We observed the nuclear region of the galaxy NGC 1365 with the integral field unit of the Gemini Multi Object Spectrograph mounted on the GEMINI-South telescope. The field of view covers $13^{primeprime} times 6^{primeprime}$ ($1173 times 541$ pc$^{2}$) centered on the nucleus, at a spatial resolution of $52$ pc. The spectral coverage extends from $5600$ AA to $7000$ AA, at a spectral resolution $R=1918$. NGC 1365 hosts a Seyfert 1.8 nucleus, and exhibits a prominent bar extending out to $100^{primeprime}$ (9 kpc) from the nucleus. The field of view lies within the inner Lindblad resonance. Within this region, we found that the kinematics of the ionized gas (as traced by [OI], [NII], H$alpha$, and [SII]) is consistent with rotation in the large-scale plane of the galaxy. While rotation dominates the kinematics, there is also evidence for a fan-shaped outflow, as found in other studies based on the [OIII] emission lines. Although evidence for gas inflowing along nuclear spirals has been found in a few barred galaxies, we find no obvious signs of such features in the inner kiloparsec of NGC 1365. However, the emission lines exhibit a puzzling asymmetry that could originate from gas which is slower than the gas responsible for the bulk of the narrow-line emission. We speculate that it could be tracing gas which lost angular momentum, and is slowly migrating from the inner Lindblad resonance towards the nucleus of the galaxy.