Mourinho is widely expected to replace current interim manager Rafa Benitez in the summer after it was confirmed the Portuguese will be leaving Real Madrid at the end of the season.
During his first spell at Chelsea, Mourinho won two Premier League titles and several other trophies in a three-year tenure before leaving in 2007.
Though Cech acknowledged there has been change in west London in the intervening period, the goalkeeper believes Mourinho would fit right back in.
"I think the club has changed since he left," Cech told Sky Sports News. "It's been six years and the club has changed through the years.
"But he knows the club, he knows the environment, he knows English football and the Premier League. I think this is a big advantage.
"He might find a slightly different club than when he was leaving, but he will still find a club full of ambition and expectation and hunger to win trophies. This is the most important thing.
"I came to the club at the same time he did and he had confidence in me to put me in goal ahead of Carlo Cudicini.
"Since then, we won so many trophies. Although he left in 2007, I think everybody around the club and the supporters still remembers him with high regard."
Chelsea's versatile Brazil international David Luiz would also welcome the chance to play under Mourinho next season.
Luiz said: "Everyone says a lot of good things about him. Everyone knows about his quality.
"He has done a great job in many clubs in the world, like with Chelsea. It is exciting when we can work with an experienced coach and a very good coach."