The 33-year-old, who won two La Liga titles, a UEFA Cup and a European Super Cup during his time with Valencia, has also insisted that he wants to end his career with Levante.
"To continue growing this club must be playing in La Primera but we must be realistic and realise our objective is to remain in the division," he told reporters at a press conference.
"Even so, I'd like to win the Copa del Rey. It's a trophy I haven't won. I now think I want to finish my playing career here and I also want to do some great things with this club, where I am very happy. It is like my family.
"My first choice was always to remain at Levante. I'd always heard from afar that it was a family and you do have some doubts, but when you arrive here you feel just like one of them."
Navarro's current contract with Levante runs until 2014.