  In this paper we extend our previous work on gluon propagator in the
Instanton Liquid Model (ILM) of the QCD vacuum. This objects presents a lot of
interest for studies of the heavy quarkonium $Q\bar Q$ observables in the
framework of potential Nonrelativistic QCD (pNRQCD). Our goal is to evaluate
the gluon polarization operator in ILM, and understand if it gets contributions
from infrared (IR) renormalons. We perform a systematic analyis, taking into
account both perturbative and nonperturbative effects, and making a double
series expansion in terms of the strong coupling $\alpha_s(\rho)\sim 0.5$ (the
scale is given by average instanton size $\rho\approx1/3$ fm) and the instanton
gas packing fraction $\lambda=\rho^4/R^4\sim 0.01$ ($R\approx 1$ fm is average
inter-instanton distance). We demonstrate that there are no IR renormalon
related to ILM gluon propagator, since instantons generate a ILM gluon
dynamical mass.
