Cech's arrival at Chelsea in 2004 coincided with Mourinho's and the goalkeeper believes the Special One is eager for more glory.
"Jose Mourinho can't be more hungry," said Cech, who was speaking at an adidas Blue Pitch project in Kuala Lumpur during the club's tour of Asia.
"He didn't come back to enjoy his life. We are all here to try to prepare and to try to win things together.
"He's the same (as before). The motivation is the same, the hunger for success is the same and you can see that the demand he has for the team is the same.
"He wants to be the best, we would like to be the best - let's see if we can fulfil our expectations."
Three players have been signed since Mourinho's return last month - Andre Schurrle, Marco van Ginkel and Mark Schwarzer, the former Middlesbrough and Fulham goalkeeper.
Cech insists that although his place has long seemed secure to outsiders, it has not been the case.
The Czech Republic international said: "I'm always under pressure. You, the media, underestimated the situation at Chelsea in the last three years with Ross Turnbull and Hilario.
"You have no idea what you're talking about in terms of goalkeepers, because everyone was saying 'we need better back-up'.
"You've never seen them training, you've never seen them working.
"There are many goalkeepers playing at different teams who don't have the quality of Hilario and Turnbull.
"They kept me always under pressure. I did my best always to play and I did so.
Back-up goalkeepers Ross Turnbull and Hilario left Chelsea this summer after their contracts were not renewed, although there has been speculation the latter might re-sign.