The veteran goalkeeper joined the Blues last summer on a one-year deal and, as expected, played as Petr Cech's understudy for most of the campaign.
However, despite making just four Premier League appearances during the season, he is keen to stay at Chelsea.
Speaking in Sydney on Wednesday, the 41-year-old said: "I've had messages from the boss, he's very keen for me to re-sign with the club.
"And that's all I really need to know, that he wants to keep me at the club and I'll leave the rest up to the powers-that-be to sort it all out.
"I'm confident it'll be sorted out in the next week or two."
The former Middlesbrough goalkeeper still has some hopes that he may yet play in the Australian A-League before he quits playing.
"I did say a couple of years ago that I'd never come back and play in the A-League - that was something I regret saying, purely on the basis that you should never say never because things do change," he said.
"It wasn't out of disrespect to the A-League, it was just that I always wanted to play at the highest level - which I do want to do.
"I still want to stay in Europe as long as possible. If I have the chance to stay at a club like Chelsea, I'd love to do so because it's an unbelievable experience.
"I had opportunities to play in the Champions League semi-final (at the end of last season) and vie for the title - and that's something invaluable and something I hadn't experienced before. And I wouldn't change anything for it."