Goal understands Barca are locked in a battle with Manchester City sign midfielder De Jong , with the Catalan outfit of the belief that the Premier League champions have stolen a march in their pursuit of the 21-year-old.
De Ligt, meanwhile, is also being pursued by City having established himself as a key member of Ajax's first team, with the 19-year-old centre-back also a target for Juventus .
And Cillessen believes the pair would be delighted to make the switch to Camp Nou, revealing he has spoken to De Ligt about the club.
"Everybody in the national team would like to play for Barcelona because it's one of the best teams in the world," the Barca goalkeeper told Sport .
"I didn't play with De Jong at Ajax, but I did play with De Ligt for a few weeks, because he came up to the first team in the summer of 2016. I was able to work with him that pre-season, before coming to Barca. He's a player with a lot of quality and is only 19.
"He's physical, strong, mentally strong, especially if you see the [Netherlands] game against Germany. In the first half he didn't go so well, but he recovered in the second half, he was excellent in the second half. He was also excellent against Bayern Munich in the Champions League for Ajax.
"I spoke with him about [Barcelona], he has the level, but he's still 19 years old … I don't know because [Marc] Overmars is in charge at Ajax, so I don't know what he wants. I also read he's not going anywhere [in January]."
Cillessen added that De Jong is an "interesting option" as a potential successor to Sergio Busquets at the heart of Barca's midfield.
"With the national team he plays more like Busquets. But Busquets is on another level at the moment," said Cillessen.
"It's an interesting option, but it's the same as with De Ligt: it depends on Overmars' opinion."
Marc-Andre ter Stegen is the first-choice keeper at Barca but Cillessen has no intention to leave and confirmed no offers have been received.
"What I want is to play at the highest level possible," he said. "But there was nothing firm. I've not had any concrete offers on the table and, on top of that, Barca told me they didn't want to lose me.
"What the club said made me feel valued. It was important for me that they showed that confidence in me.
"We didn't speak with any [other] club in a concrete way, there was nothing solid."