The Springbok star believes the Cape side have every reason to be confident after coming agonisingly close to knocking out Toulon in last season's round of 16, losing by just one point.
Their quarter-final appearance in 2022/23 also showed the Stormers can compete with Europe's best.
"We showed tremendous form last year in the Champions Cup. And going to Toulon, we lost by one point. So we feel very strongly about this competition," Willemse told reporters on Wednesday.
"We, as a club, have made a decision that we obviously want to go further than the quarterfinal."
The Stormers will begin their campaign at home for the first time when they host Bristol Bears in Cape Town on Saturday, giving them an opportunity to make an early statement in front of their own supporters.
However, the challenge will not ease after their opener, with away fixtures against defending champions Union Bordeaux Begles and Gloucester followed by a home clash against Racing 92.
"We're going to Gloucester, we're going to Bordeaux, and these are all tough games. We're playing against the best clubs in Europe," Willemse said.
"We've got great fixtures this year, so we're looking forward to that."
For Willemse, the ultimate ambition is to secure the silverware that would bring a European star to the Stormers' jersey.
"On a personal level, I think I firstly just want to help the team get to that stage. And then, obviously, for us as a club, it would mean the world for us to add a star to our badge," he said.
Having experienced the demands of knockout rugby against Europe's leading clubs, Willemse believes the Stormers know what is required to make another deep run in the competition.
"We've gone to the quarterfinals, we've played in the round of 16, so we kind of know how and what the pressure and everything feels like when you go to Europe and you play the big, mega clubs in Europe, like Bordeaux, Toulon or Leinster," he said.
Willemse expects Bristol to provide a stern opening test, pointing to the English side's attacking quality and versatility.
"There's a lot of firepower in the backline. Louis Rees-Zammit, Gabriel Ibitoye, Tom Jordan is a massive player. Bernhard Janse van Rensburg is there. They've got the full package team," he said.
"They're an outstanding team. They can move the ball, they can kick, they can run. So, yeah, it's going to be a massive clash on Saturday."
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