Navas signed for City from Sevilla in June along with Alvaro Negredo and has started each of City's three Premier League fixtures so far this season.
Joe Hart has been an ever-present first choice at the Etihad Stadium for the past three seasons, but has come under fire in recent months after a series of mistakes.
"He (Casillas) would be a great signing for City," Navas told Movistar. "You always want great players in your team because they can be so important.
"We are not suddenly thinking this about Iker though. We all know what a great keeper he is and how vital he is to his team."
"I am very happy and have been so since the first minute," he continued. "It was an opportunity that I wanted to take, I like English football a lot because of the style of play and the speed of it.
"City is a team that should aspire to win everything, we are strong and have to have confidence and we should remain calm.
"We have started well in the league although our main aim is the Champions League because we want to go a long way in the competition."
