The 22-year-old has made just five appearances since joining on loan from Barcelona in the summer after suffering from knee injuries.
The Spaniard played the final nine minutes of Ajax's 2-0 win at NAC Breda - a victory which saw them maintain their four-point lead at the top of the Eredivisie table.
Cuenca impressed on his return to the side and is keen to help Ajax to glory this season and next.
"I want to stay another year at Ajax," he told De Telegraaf.
"FC Barcelona know what I want and the clubs are talking about it, because relationships are good, I trust that I stay.
"Because of my injury I can not play much, but next season I want 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 under Frank de Boer and play."