The Argentinian goalkeeper was in superb form on Saturday as the Eagles claimed a 2-0 FA Cup third-round triumph at West Brom, turning in a man-of-the-match performance with a string of fine saves after the break to deny the hosts.
Speroni duly claimed his 93rd clean sheet since joining the south London club in 2004 - a 10-year anniversary he will celebrate this summer.
But that is also when his current deal at Selhurst Park expires and the 34-year-old insists there has not yet been any movement on fresh terms.
"No, we haven't spoken as of yet so I don't know what's going to happen," he said.
"I love this club. I've been here 10 years now. But in football you never know."
Manager Pulis, who has only been in charge of Palace since early November, is one of several bosses to have been linked with a potential January move for Wolves 'keeper Wayne Hennessey.
But he has suggested there could be a new deal for Speroni before the end of the season.
Pulis said: "Speroni, along with half a dozen of the other players, has been absolutely superb since I have come into the club.
"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."