The Blaugrana youth product has suffered with injury problems at times this season, meaning he has made only a handful of appearances for the club.
As a result Cuenca is determined to remain at the Amsterdam Arena beyond the campaign and is confident he will get his wish.
"I want to stay another year at Ajax," the 22-year-old told De Telegraaf.
"Barcelona know what I want and the clubs are talking about it. Because relationships are good, I trust that I will stay.
"Because of my injury I have not been able to play much, but I want next season to be important. I have had fun with Ajax, feel comfortable and their style of play resembles that of Barca. I think it's good for my development - it is a year to train and play under Frank de Boer.
La Masia academy graduate was first picked up by the Spanish giants at the age of 12 and moved to Amsterdam at the end of the January transfer window in a move that was originally meant to last until the end of this season.
Ajax could be crowned Eredivisie champions if they defeat Willem II in their next league game.