The KNVB Beker last-16 game at the Amsterdam ArenA is a rerun of the match which was abandoned before Christmas when AZ goalkeeper Esteban Alvarado was attacked by a fan.
Alvarado was sent off after retaliating, prompting Verbeek to withdraw his players from the pitch and the match to be abandoned.
Initially the KNVB ordered tomorrow's game to be played behind closed doors, but relented and the match will now be played in front of a crowd consisting mainly of children from local schools and sports clubs, with a limited number of adults allowed in as chaperones.
"I am glad that at least some fans will be coming," Verbeek told www.az.nl. "I've had experience as coach of Heracles Almelo of playing in an empty stadium against NAC.
"I found the atmosphere was very grim and gloomy. That's especially true in a big stadium, and the Arena is something even more than that."
With around 20,000 children expected in the stands, Ajax boss Frank de Boer concurred with his opposite number.
He told www.ajax.nl: "It is obviously better than an empty stadium, though we naturally would prefer our own supporters to be there.
"The presence of all those children will probably create a lot of noise in the stands - and I should know, because I'm the father of three daughters."
Three days after tomorrow's game, the pair meet again in the Eredivisie at the AFAS Stadion, home of the league leaders.
While Verbeek is keen to see his side progress, he also knows there could be a secondary benefit from a positive result tomorrow.
"The winners of first the contest will gain confidence to take into Sunday's game," he told www.az.nl. "But Thursday is about earning a place in the next round. This is the focus the group should have."
The winners of tomorrow's tie will face amateur side GVVV in the quarter-finals.