Mourinho became the most successful manager in Chelsea's history between June 2004 and September 2007, which included the Blues' first championship in 50 years.
The self-styled Special One went on to win the Champions League at Inter Milan and punctuated the Barcelona hegemony at Real Madrid by winning the 2011/12 Primera Division.
But Cech, whose arrival at Chelsea in 2004 coincided with Mourinho's, says his manager is eager for more glory now he has returned to Stamford Bridge.
"Jose Mourinho can't be more hungry," said Cech. "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."
Mourinho has been successful wherever he has managed and won the Europa League and Champions League at Porto before moving to Stamford Bridge nine years ago.
Champions League success was elusive for the Portuguese at Chelsea, but the club did lift the most prestigious title in European club competition in 2012.
However, the Blues last season suffered the ignominy of becoming the first holders to exit the competition at the group stages, before lifting the Europa League, while their last Premier League title was in 2010.
Managers have been hired and fired since Mourinho's departure and the Portuguese has spoken of the need for stability and his wish to be in west London long-term.
"We need trophies (for stability)," Cech said. "If we fulfil our targets, for sure we will keep the same manager. We will have a go. We will try to win as much as we can. We will count the trophies at the end of the season.
"A club of the size of Chelsea Football Club, you need to target as best as possible and see if you can make it or not. Last season we won the Europa League; it was the first time the club had played in the competition and we managed to win it.
"It was a successful campaign, but obviously our target is to play better in the Champions League than we did last season. If we can challenge the teams to win it, we will try to do it."
Chelsea have won the Premier League once since Mourinho's exit, but the competition is not necessarily a bigger priority than any other.
Cech said: "We always want to win the Premier League. The last two campaigns in the Premier League were not the ones we wanted and we want to do better."