The Czech Republic international has seen his team win just one title in the 2009-2010 season since Jose Mourinho’s first departure from the club.
“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.”
The Blues sealed a convincing 3-1 victory against Norwich before heading into the international break. Arsenal are currently on top of the table with Chelsea trailing by two points.
Chelsea lack depth up front and the match against Norwich was their first away win this season, having previously drawn 1-1 with rivals Tottenham.
Chelsea will host Cardiff at Stamford Bridge on Saturday after which they will travel to Germany to play their UEFA Champions League match against Schalke 04 on Tuesday.
Germany is a special place for Chelsea as they triumphed over Bayer Munich to win the Champions League in 2012.
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.”
The 31-year-old is one of the four players, the others being John Terry, Ashley Cole and Frank Lampard, to still remain with the club during Mourinho’s second stint as Chelsea manager.
Terry, Cole and Lampard will become free agents next season but could end up signing new contracts.
Chelsea boss Jose Mourinho has called for the club to produce more homegrown players and has heaped praise on Nathaniel Chalobah, who had a fruitful loan spell at Watford and is now temporarily at Nottingham Forest.
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).”
Ashley Cole who was out of the Three Lions matches against Montenegro and Poland due to a rib injury may not feature for Chelsea against Cardiff.