The Cairo giants progressed as the best second-placed team across the three groups, securing their spot in the final four based on goal difference.
Under tournament regulations, the group winners and the best runner-up advance to the semi-finals.
Ahly, second in Group B with two points and a goal difference of +18, edged out UAE's Sharjah HC (2 points, -5) and local rivals Zamalek (2 points, -20) to claim the final semi-final slot.
Zamalek were eliminated after a heavy 47-25 loss to Spanish giants Barcelona, who topped Group C.
Ahly will face Barcelona, winners of Group C, in Tuesday’s semi-final, while Veszprem take on three-time world champions SC Magdeburg of Germany earlier in the day.
Last year, Ahly made history by defeating Barcelona 32-29 in the third-place match, becoming the first non-European club to beat the record five-time Super Globe winners and 12-time European champions.
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