The shot-stopper, who has maintained that he wants to stay at the club, comes to the end of his current contract in the summer.
"At the moment I just have to see what happens," the Croydon Advertiser quotes Speroni as saying. "I can't thank the fans for all their support and I know they want me to stay.
"I want to stay and I think the club wants me to stay as well. We need to sort things out. When? I'm not really sure. There have been some talks, but I don't think it's going to happen any time soon."
Speroni received plaudits for his performance during Palace's 1-0 victory over Chelsea last Saturday.