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.
And Navas has called on international team-mate Casillas to join the collection of Spaniards in Manchester if he is considering leaving Real Madrid, for whom he has not played since January.
"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."
The 27-year-old is enjoying life in the Premier League, having previously suffered with homesickness that stopped him from travelling with the national side.
However, having overcome his issues, Navas is only thinking about his game and is targeting success in the UEFA Champions League after consecutive group-stage exits for City in the past two campaigns.
"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."
