The goalkeeper has spent the last 10 years at Selhurst Park but his contract is due to expire at the end of the season.
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"Speroni, along with half a dozen of the other players, has been absolutely superb since I have come into the club [in November]," the Welshman told reporters.
"Of course [I would like to keep him] and he has been at the club how long? For 15 years? Or 120 years, or whatever it is."
Speroni has made no secret of his affection for Palace but is unsure of whether he will stay.
"We haven't spoken [about a new contract] as of yet so I don't know what's going to happen," the keeper remarked.
"I love this club. I've been here 10 years now but, in football, you never know."