The Large Hadron Collider (LHC) at the European Organisation for Nuclear Research (CERN) will be upgraded to further increase the instantaneous rate of particle collisions (luminosity) and become the High Luminosity LHC (HL-LHC). This increase in luminosity will significantly increase the number of particles interacting with the detector. The interaction of particles with a detector is referred to as "hit". The HL-LHC will yield many more detector hits, which will pose a combinatorial challenge by using reconstruction algorithms to determine particle trajectories from those hits. This work explores the possibility of converting a novel graph neural network model, that can optimally take into account the sparse nature of the tracking detector data and their complex geometry, to a hybrid quantum-classical graph neural network that benefits from using variational quantum layers. We show that this hybrid model can perform similar to the classical approach. Also, we explore parametrized quantum circuits (PQC) with different expressibility and entangling capacities, and compare their training performance in order to quantify the expected benefits. These results can be used to build a future road map to further develop circuit-based hybrid quantum-classical graph neural networks.