The goalkeeper is eager for a sustained title challenge after Chelsea fell short in recent years, with just one title since the end of Jose Mourinho's first spell as boss in September 2007.
"We haven't won the Premier League for three years in a row, so I think it would be great to get that back," Cech told Sport magazine.
"We have some young players, some new players who have never won the league, so it would be a great step forward for them to come and accomplish that."
Chelsea entered the international break with a 3-1 win at Norwich to move third in the Premier League standings, two points behind leaders Arsenal.
The win at Carrow Road was the Blues' first away from home in the top flight this term after a start to the campaign which has seen only flashes of their full potential.
Next Mourinho's men play a Cardiff side who have endured a fractious international break amid speculation over the future of boss Malky Mackay, before travelling to Gelsenkirchen for Tuesday's Champions League Group E clash with Schalke.
It was in Germany - in Munich, to be precise - that Chelsea won the Champions League and Cech is targeting further success in the competition.
He added: "We know how sweet it is to win the European Cup, too, so if we could go far in that and really challenge for the title, then that would be great."
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- Jose Mourinho