Alex Pastoor's side head to Philips Stadion full of confidence after winning their last three Eredivisie matches, including Sunday's 2-0 triumph over ADO Den Haag, to climb to 11th in the standings.
They will face a top-of-the-table PSV team in equally good form, but Van der Velden reckons his side should go into the match convinced they can cause an upset.
The 30-year-old told voetbalcentraal: "It will not be easy, but we are on a good run.
"It's always nice to play against such teams because they want to play good football.
"It will be tough, but it is cup football and anything can happen - and we will have that in mind when we go to Eindhoven on Thursday."
The last-eight meetings kick off on Tuesday night at the Gelredome when Vitesse Arnhem host Heerenveen, with the visitors fancying their chances of going all the way.
Jeffrey Gouweleeuw told his club's official website: "We have a real opportunity to reach the cup final.
"I think Heerenveen and Vitesse are quite similar to each other. It remains to be seen exactly how Vitesse will play. Maybe they'll leave themselves open given their desire to go forward.
"I expect at least a nice match. And, yes, Heerenveen as the winners!"
The other two-quarter-finals take place on Wednesday and see AZ Alkmaar take on third tier GVVV Veenendaal - the only non-Eredivisie side left in the competition - while Heracles Almelo face RKC Waalwijk.
AZ lost ground in the title race over the weekend with a 2-0 loss at Roda JC, but midfielder Maarten Martens insists nobody at the AFAS Stadion is pressing the panic button.
"A defeat is very annoying, but there really is not a man overboard," he told AZ's website. "We just move on."
