The 29-year-old has been a mainstay for the west Londoners since joining from French club Rennes for ?7million in 2004.
Reports suggested Andre Villas-Boas could sell Cech in favour of summer signing Thibaut Courtois - currently on loan at Atletico Madrid - but the Czech international is keen to sign a new contract, telling the London Evening Standard: "Yes, I think [I will sign a new deal] and we will not have a problem."
He added: "There are a lot of matches at this time of year so we agreed [before Christmas] that both sides would prepare for the negotiations and meet to resolve it when there is time for that.
"The last few weeks have been hectic and we [agreed] to meet after New Year's Day. I have been here for seven years and I have been more or less a regular starter, so I'm more than happy to stay.
"Ever since I was a kid I wanted to be at a club who are among the best in the world. Chelsea are in the world's top competition, so I have no reason to leave. I would like to see myself staying here."
While Cech is keen to commit his immediate future to the Stamford Bridge club, he refused to rule out one day plying his trade elsewhere.
"It is difficult to leave the best league in the world and if you take a look around, you will not see many teams of Chelsea's category that would be looking to sign a new goalkeeper," Cech added.
"If I would like to try something new, then it would have to be a club of a similar level to Chelsea.
"You never know, everything happens fast in the football life. You can sign a 10-year contract with a club and then end up leaving after three years. I'm 29 years old and I believe that there is still time for a possible change."