  We study the renormalization of a complete set of gauge-invariant gluon
nonlocal operators in lattice perturbation theory. We determine the mixing
pattern under renormalization of these operators using symmetry arguments,
which extend beyond perturbation theory. Additionally, we derive the
renormalization factors of the operators within the modified Minimal
Subtraction $(\rm \overline{MS})$ scheme up to one-loop. To enable a
non-perturbative renormalization procedure, we investigate a suitable version
of the modified regularization-invariant (${\rm RI}'$) scheme, and we calculate
the conversion factors from that scheme to $\rm\overline{MS}$. The computations
are performed by employing both dimensional and lattice regularizations, using
the Wilson gluon action. This work is relevant to nonperturbative studies of
the gluon parton distribution functions (PDFs) on the lattice.
