High-energy neutrino observation from the Seyfert galaxy NGC 1068 offers new insights into the non-thermal processes of active galactic nuclei. Simultaneous gamma-rays emitted by such sources can possibly oscillate into axion-like particles (ALPs) when propagating through astrophysical magnetic fields, potentially modifying the observed spectrum. To probe for ALP-induced signals, a robust understanding of the emission processes at the source is necessary. In this work, we perform a dedicated multi-messenger analysis by modeling a jet in the innermost vicinity of the central supermassive black hole of NGC 1068. We model in particular the neutrino and gamma-ray emission originating in lepto-hadronic collisions between jet accelerated particles and background particles from the corona, reproducing both the Fermi-LAT and IceCube data. These source models serve as a baseline for ALP searches, and we derive limits on the ALP-photon coupling by marginalizing over motivated ranges of astrophysical parameters. We find gaγ≲7×10−11GeV−1 for ma≲10−9 eV. These limits may be weaker than existing constraints, but they demonstrate the potential of multi-messenger observations to probe new physics. We conclude by discussing how additional upcoming multi-messenger sources and improved observational precision can enhance ALP sensitivity.