The respective contribution of disc and jet components to the total emission in low-luminosity active galactic nuclei (LLAGNs) is an open question. This paper suggests that γ-rays emitted from electrons accelerated in jets could be a direct diagnostic tool for a jet component to the total emission. We demonstrate γ-ray flux from jets based on a synchrotron self-Compton model on the assumption that radio and X-rays are dominantly produced from jets in the case of a high state of a nearby LLAGN, NGC 4278. We also survey parameter space in the model. Observational properties of LLAGNs in radio and X-ray bands allow to constrain physical parameters in an emission region. The size of the emission region R is limited to 1016≤R≤ 1017.5 cm if the observed tight correlation between radio and X-ray emission originates from the same jet component. If the beaming factor of the emission region is close to the observed parsec scale jet of NGC 4278 and R∼ 1016 cm, the γ-rays may be detected by the Cherenkov Telescope Array and the jet domination can be tested in the near future.