Recent observational data show that the Milky Way galaxy contains about 170 globular clusters. A fraction of them is likely formed in dwarf galaxies accreted onto the Milky Way in the past, while the remaining of clusters are formed in-situ. Therefore, different parameters, including orbits, of the globular clusters is a valuable tool for studying the Milky Way evolution. However, since the evolution of the 3D mass distribution of the Milky Way is poorly constrained, the orbits of the clusters are usually calculated in static potentials. In this work, we study the evolution of the globular clusters in several external potentials, where we aim to quantify the effects of the evolving galaxy potential on the orbits of the globular clusters. We specially estimate the dynamical evolution of the interaction of globular clusters' with the Galactic centre that dynamically changed in the past. For the orbits calculation we used five Milky Way-like potentials from IllustrisTNG-100 simulation database, which were selected for their similarity to the present-day Milky Way, to simulate the structure of the Galaxy at different times. The orbits of 159 globular clusters were integrated using a high-order N-body parallel dynamic code phi-GPU, with initial conditions obtained from recent Gaia Data Release 3 catalogues. To distinguish globular clusters interacting with the Galactic centre, we used the criterion of a relative distance of less than 100 pc. We obtained approximately three to four globular cluster interactions per billion years at distances of less than 50 pc and approximately five to six interactions per billion years at distances of less than 80 pc among the studied 147 globular clusters that had close passages near the Galactic centre. We selected ten of them for detailed study and found almost 100% probability of an interaction with the Galactic centre for six of them.