The 34-year-old Argentine shotstopper, who joined the Eagles in 2004, is out of contract in the summer.
Speroni has now suggested that he will leave Selhurst Park in the coming months if he is not offered a new deal.
"I am not sure what is going to happen next season," Speroni is quoted as saying by Sky Sports News.
"From now on I can start thinking ahead. Before I was concentrating on keeping Palace in the Premier League - that was the main target. I think now we can sit down and think what is going to happen next.
"I'm free to talk to other clubs in Europe. I am confident I will be playing for the next three or four seasons. But where, who knows?"
Palace continue their Premier League campaign on Sunday when they entertain Manchester City.