Borussia Dortmund have made their first signing after Jurgen Klopp's departure by landing midfielder Gonzalo Castro.
The Argentinian goalkeeper has become a fans' favourite since arriving at Selhurst Park from Dundee in 2004.
Speroni has made 343 appearances for the Eagles in that period and has been one of their key performers during their return to the Barclays Premier League.
However, despite such fine displays and talk of a late World Cup call-up, the 34-year-old's future remains unclear as his deal expires at the end of the season.
The January arrival of Wayne Hennessey from Wolves also raised questions, but Speroni remains intent on staying at Selhurst Park.
"That is my priority," he told reporters. "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."