The 40-year-old Australia goalkeeper became Jose Mourinho's third summer signing, three years after a move to Arsenal failed to materialise.
Schwarzer, who has spent 15 years in England with Bradford, Middlesbrough and the Cottagers, said: "When I moved to Fulham I thought that was it and then the Arsenal thing popped up so after that experience I said 'Never say never'.
"It's proven to be true. I still say 'Never say never'. It's not over until it's over."
Schwarzer will be 41 in October, but has the 2014 World Cup in his sights and believes he is playing as well as ever.
"I am 40 years old but I feel incredibly well and I am holding my own, no problems whatsoever," he added.
"I feel incredibly fit and I love playing football. As long as I am playing well enough at this level I will continue to play.
"The aim is to continue to get better; I don't want to stop getting better.
"If you stop getting better then it is a downward slippery slope."
Schwarzer became aware of Chelsea's interest towards the end of last season before signing a one-year deal earlier this month after speaking to Mourinho.
The Australian will compete with Petr Cech for the number one jersey, but will likely begin the season as second choice.
Nevertheless, he is determined not to spend the campaign sitting on the substitutes' bench.
"Before I spoke to the manager I had some doubts, but once I spoke to the manager those doubts disappeared pretty quickly," Schwarzer said.
"The amount of games Chelsea play there is going to be opportunities to play games and that's also important for me."
Cech has welcomed Schwarzer, who joined up with his team-mates in Bangkok and made his first appearance against a Malaysia XI in Kuala Lumpur last weekend.
"He's a great goalkeeper and a good guy," said Schwarzer, who is likely to be granted a further opportunity to play in Jakarta tomorrow in the final match of Chelsea's Asia tour.
"He has been extremely accommodating for me since I have arrived. It's been great to work alongside him.
"Hopefully I can learn from him and maybe he might learn from me too. I think we can complement each other very well."
The Australian has avoided discussing cricket with his new team-mates, particularly Frank Lampard, given England lead the Ashes series 2-0.
"Frank's a big fan," Schwarzer said.
"I try not to talk to him about it too much because it's not looking good for us."