Jose Mourinho's men top the Premier League with 39 points from 16 matches and have lost just once in the top-flight this term.
Tuesday's 3-1 victory at Derby County also put the London club through to the semi-finals of the League Cup, where they will meet Liverpool.
An unprecedented quadruple is not out of the question, with Chelsea set to take on Paris Saint-Germain in the last 16 of the UEFA Champions League, and Watford in the FA Cup third round.
Goalkeeper Cech, who has largely played second fiddle to Thibaut Courtois at Stamford Bridge this term, has challenged the team to live up to their potential by securing silverware.
"This team has the potential and the quality to become one of the best teams in Chelsea's history if it proves it by winning the trophies," said Cech, who has been at Chelsea since 2004.
"But I keep saying you can only judge teams at the end of the season when you see how much the team achieve.
"In this moment, we have been doing remarkably well but we have no trophy in our hands. So let's see what's going to be the case at the end of the season.
"We want to win as many games as possible, as many competitions as possible, then let's see what it's going to bring us.
"It is difficult to know how many of them you can actually manage to win.
"You cannot say, 'We leave this competition, we chase that competition' because in the competition you pick you have one unlucky game and you have nothing. So you can't treat competitions like that.
"We progressed in the Champions League, our aim, we've progressed in the League Cup, we are top of the league, so far we are doing well."
