Speroni's place in the side is at threat from Wayne Hennessey, who signed from Wolverhampton Wanderers in January, but the 34-year-old admits that he would prefer to stay at the club and fight for his spot.
"During my time here I am used to different managers arriving and other goalkeepers coming in," Speroni told reporters.
"I've always seen that as a challenge and I've always kept my place in the side. This is no different.
"I'm happy with my form this season. I have felt fitter and better than ever. I have a good few years left and hopefully everything will be tied up soon."
Speroni, whose current deal expires in the summer, joined Palace from Dundee in 2004.