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."
Managerless West Brom are still searching for a successor to Steve Clarke, who was sacked on December 14.
Caretaker head coach Keith Downing, who does not want the position full-time, tasted the first defeat of his five-match spell in charge against Palace.
It remains to be seen what the future holds at The Hawthorns and who or when a new boss will be installed.
Albion striker Shane Long said: "Obviously Keith and Dean (Kiely) have come in and they've done a terrific job.
"It's their first loss here. They've picked up six points out of the four league games so we've done very well since they've been in there and all the lads know them as well.
"But I think a bit of clarity for all the players, to get the new manager in, to understand what the rules are going to be with a new manager in charge.
"It's a new lease of life. People want to impress him.
"We'll see what happens but the lads are playing well for Keith so if they stay in for a little bit longer, it might do us good as well."