The winger joined Manchester United in a £15m deal in January 2013 before returning to Selhurst Park on a temporary deal until the end of last season.
His opportunities to impress have been limited under new United boss David Moyes, with Zaha making just four appearances for the club during the current campaign.
That has alerted Pulis to his possible availability, although the former Stoke manager was keen to stress that the final decision on whether Zaha is allowed to go out on loan lies with Moyes.
"Obviously he was a tremendous player at this football club and United spent a lot of money on him. I'm sure Wilfried and David and Manchester United will decide what they want to do," he said.
"We'd be interested, whether we could do it, but we'd be interested if the player was available.
"We're cutting across a line I really don't want to go past, you're talking about other players who are owned by other football clubs. That's disrespectful to United and especially David."
Newcastle have also been linked with the 21-year-old England international but United manager Alan Pardew was also keen to keep a respectful distance.
"He's a Manchester United player, as far as I am concerned, but he is a player I know well because obviously he played for my old team Palace," said Pardew.
"He was absolutely phenomenal when they were promoted and got the big move to United.
"Unfortunately, that career has stalled a little bit, but that's a growing process as well.
"I know he has done very well at Manchester United in the background and maybe he will get an opportunity there."