Speroni is keen to stay with Palace but his future remains unclear as his current deal with the club expires at the end of the season.
The 34-year-old, who has made 343 appearances since signing from Dundee in 2004, has been a star performer for Palace since their return to the Premier League.
The January signing of Wayne Hennessey from Wolves also raised questions about Speroni's future but the Argentinian is intent on staying at Selhurst Park.
"That is my priority," he said. "At the moment I don't know what's going to happen.
"As a professional footballer I need to understand different situations and I can't say any more than that.
"As a player you prefer to sort things a lot earlier but sometimes you have to adapt to how the circumstances go.
"At the moment I just have to see what happens. I 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."