We report hints for the correlation between the X-ray and $\gamma$-ray emission in the nearby galaxy NGC 4945, which harbors both an active galactic nucleus and a nuclear starburst region. We have divided the Fermi/LAT observations of NGC 4945 into two datasets, comprising events detected during the low (L) and high (H) level of X-ray emission from the active nucleus of this galaxy, determined using the Swift/BAT light curve. Both datasets contain an equal amount of 3.8 years of LAT data and NGC 4945 is detected with a similar statistical significance of $\sim 15 \sigma$ in L and $14 \sigma$ in H. However, the slope of the $\gamma$-ray spectrum hardens with the increase of the X-ray flux, with the photon index $\Gamma = 2.47 \pm 0.07$ in L and $2.11 \pm 0.08$ in H. The change is confirmed by a systematic variation of the spectral energy distribution as well as a substantial reversal of the $\gamma$-ray signal in significance maps for low and high $\gamma$-ray energies. The X/$\gamma$-ray correlation indicates that the $\gamma$-ray production is dominated by the active nucleus rather than by cosmic rays interacting with the interstellar medium. We discuss possible locations of the $\gamma$-ray source. We also compare NGC 4945 with other starburst galaxies detected by LAT and we note similarities between those with active nuclei, e.g. unlikely high efficiencies of $\gamma$-ray production in starburst scenario, which argues for a significant contribution of their active nuclei to the $\gamma$-ray emission.