  We present the results that are necessary in the ongoing lattice calculations
of the gluon parton distribution functions (PDFs) within the pseudo-PDF
approach. We give a classification of possible two-gluon correlator functions
and identify those that contain the invariant amplitude determining the gluon
PDF in the light-cone $z^2 \to 0$ limit. One-loop calculations have been
performed in the coordinate representation and in an explicitly gauge-invariant
form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources
of the $\ln (-z^2)$-dependence at short distances $z^2$. The UV terms cancel in
the reduced Ioffe-time distribution (ITD), and we obtain the matching relation
between the reduced ITD and the light-cone ITD. Using a kernel form, we get a
direct connection between lattice data for the reduced ITD and the normalized
gluon PDF. We also show that our results may be used for a rather
straightforward calculation of the one-loop matching relations for quasi-PDFs.
