The Ajax skipper has been linked with numerous European heavyweights on the back of an impressive campaign with the Dutch giants.
Cillessen, who made the switch from Ajax to Barcelona three years ago, has told his compatriot to think carefully about his next career step.
"I sat down with him to talk about all his options, the same as I did with Frenkie [de Jong]," he said in an interview with Mundo Deportivo.
"I told him that the decision belongs to him. Matthijs is a good boy and he knows what he has to do.
"I told him that I could not make the decision for him - he knows what he has to do. I can only talk about good things about Barca because it's a great club and I have a great feeling with Barca."
Should De Ligt make the move to Camp Nou he will have to compete with Gerard Pique, Clement Lenglet and Samuel Umtiti for a starting spot, but Cillessen insists the 19-year-old is good enough to make the grade with the La Liga champions.
"He has many qualities," Cillessen added.
"He is very young, he is only 19 years old. Barcelona needs players with a very high level and he has the level to play there."
Cillessen's own future is in doubt after revealing in April that he is looking for a new club, having played second fiddle to Marc-Andre ter Stegen over the past three seasons.
Asked for an update on his situation, amid rumoured interest from fellow La Liga side Valencia, he said: "At the moment I do not know what is going to happen.
"After the Nations League I will go on vacation with my friends and we will see what happens.
"Valencia are a great team, but I do not know what will happen because I have not talked to my agent yet.
“I only know what I read in the newspapers and on the internet. I will do it after the final and enjoy my vacation."