The goalkeeper, who will make his 300th Premier League appearance when Chelsea host Cardiff on Saturday, is eager for a sustained title challenge after falling short in recent years, with just one crown 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.
Mourinho's men now play a Cardiff side who have endured a testing international break amid speculation over the future of boss Malky Mackay, before travelling to Gelsenkirchen for Tuesday's UEFA 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."
Cech is one of the survivors of Mourinho's first spell as boss. Three others - captain John Terry, Ashley Cole and Frank Lampard - are all out of contract at the end of the current campaign.
The trio could yet earn new deals, but whatever happens Mourinho hopes the Blues will produce another homegrown core of talent.
Mourinho has been fulsome in his praise of the likes of Nathaniel Chalobah - now on loan at Nottingham Forest but told he will be part of the Chelsea first team next season - and is optimistic the club's academy can bear further fruit.
Mourinho told the Guardian: "Ideally it's not just about having British players either, but having players who are made in Chelsea.
"In three or four years' time, if we don't have other Englishmen to replace this nucleus of players - when Lamps is 39, John is 36 - I will be very sad. Every club needs that. So we are working on that (new generation)."
Left-back Cole is doubtful for the Cardiff clash after missing England's World Cup qualifying successes over Montenegro and Poland with a rib injury.