Cillessen has been linked with a switch to the Premier League club to reunite with his former coach at Ajax, Frank de Boer, who has taken over at Selhurst Park.
The 28-year-old started a single La Liga game last season as he played second fiddle to Marc-Andre ter Stegen.
But despite his lack of action, the Netherlands international says he is not looking to leave Barcelona.
"I have not spoken with Frank, I know him well but I've not talked to him," Cillessen said on Thursday. "I'm not going. I am very happy here."
Cillessen is the Netherlands number one and the goalkeeper is assured he does not need to leave Barca for regular football after having talks with international coach Dick Advocaat.
"I spoke a lot with the new Dutch manager and he said the quality has to show every day and that's what I did," Cillessen said.
"I think I did, anyway. I played the two [Netherlands] games [in the international break] and that's what I do on the training ground and in the cup games here [with Barcelona].
"I want to play more, but that depends on the coach [Ernesto Valverde]. All players want to play more."