  NGC 1068 is a nearby widely studied Seyfert II galaxy presenting radio,
infrared, X- and $\gamma$-ray emission as well as strong evidence for
high-energy neutrino emission. Recently, the evidence for neutrino emission
could be explained in a multimessenger model in which the neutrinos originate
from the corona of the active galactic nucleus (AGN). In this environment
$\gamma$-rays are strongly absorbed, so that an additional contribution from
e.g. the circumnuclear starburst ring is necessary. In this work, we discuss
whether the radio jet can be an alternative source of the $\gamma$-rays between
about $0.1$ and $100$ GeV as observed by Fermi-LAT. In particular, we include
both leptonic and hadronic processes, i.e. accounting for inverse Compton
emission and signatures from $pp$ as well as $p\gamma$ interactions. In order
to constrain our calculations, we use VLBA and ALMA observations of the radio
knot structures, which are spatially resolved at different distances from the
supermassive black hole. Our results show that the best leptonic scenario for
the prediction of the Fermi-LAT data is provided by the radio knot closest to
the central engine. For that a magnetic field strength $\sim 1\,\text{mG}$ is
needed as well as a strong spectral softening of the relativistic electron
distribution at $(1-10)\,\text{GeV}$. However, we show that neither such a weak
magnetic field strength nor such a strong softening is expected for that knot.
A possible explanation for the $\sim$ 10 GeV $\gamma$-rays can be provided by
hadronic pion production in case of a gas density $\gtrsim
10^4\,\text{cm}^{-3}$. Nonetheless, this process cannot contribute
significantly to the low energy end of the Fermi-LAT range. We conclude that
the emission sites in the jet are not able to explain the $\gamma$-rays in the
whole Fermi-LAT energy band.
