Ivica Olic looks to be on his way back to Hamburg, with Andre Schurrle increasingly likely to join Wolfsburg.
Navas, who completed a £14.9m move from Sevilla this week, knows all about the Chilean, having contested a string of La Liga games with his former Malaga and Villarreal sides.
Pellegrini was finally confirmed as Roberto Mancini's successor on Friday and Navas reckons his fellow new arrival will make a smooth transition to Premier League football.
"Everything I know about him is positive. Every team he coaches plays well, and everyone in the city will support him," Navas told City's official website.
"He's important because he will help the team and we all know the importance of a good manager and a good person that we trust.
"I think (his teams are good) defensively as well.
"He clearly knows how to take a team, work hard, and get the most out of us."
Navas will join compatriot David Silva at Eastlands but says he cannot wait to test himself against some of Spain's other exports.
"I'm looking forward to playing against the Spanish players that are here - (Santi) Cazorla, (Nacho) Monreal, (Pepe) Reina, (Fernando) Torres, (Juan) Mata, and then doing well in such a good league," he added.
"It's a great league. There are players who are known all over the world playing in the Premier League."