The Brazilians finished last season empty handed after losing the Nedbank Cup final to SuperSport United, while the Dube Birds also missed out on a trophy as they finished the PSL campaign as runners-up behind Orlando Pirates.
The fact both teams came so close to securing titles last term leaves Neeskens believing the hunger for success will be running rife in both squads, which should equate to a pulsating first-leg encounter at the Lucas Moripe Stadium.
"Swallows finished as runners-up last season, and they would obviously have ambitions to win something this year. We also want the same," the Dutchman told The Sowetan.
"Everybody grabbed their chances last season, and it's time for us to grab ours in these two games (first and second leg)."