The Eagles boosted their chances of securing top-flight survival by clinching a 1-0 victory over Chelsea last weekend.
Palace are five points above the drop while their Welsh opponents reside third from bottom, three points adrift of safety.
"It was wonderful to see Cardiff get promoted last year," Pulis said in Thursday's press conference. "It was a really good year for Welsh football and I want it to thrive.
"It's a great club, a fantastic city and you hope that they stay in the Premier League along with us."
Palace have a game in hand on Cardiff, who have six games remaining in their campaign.