Calleri advanced to his sixth quarterfinal of the year by beating Frenchman Olivier Patience 6-2, 7-5, and El Aynaoui, 36, beat Slovakian Dominik Hrbaty 6-3, 7-5. El Aynaoui won this tournament in 2002.
Calleri and El Aynaoui will meet Thursday.
In other second-round action, fourth-seeded Frenchman Marc Gicquel defeated former top-five star Guillermo Coria of Argentina 6-1, 2-6, 7-6 (7-2), and French qualifier Gilles Simon beat Serbian Boris Pashanski 3-6, 6-4, 6-3. Gicquel and Simon will meet in an all-French quarterfinal.