Pulis is one of five Premier League managers to enquire about a temporary deal for Palace academy product Zaha, who completed a £15m move to United last January but stayed on at Selhurst Park to help secure promotion via the play-offs.
The England forward is yet to start in the league for his new club, and David Moyes is considering whether to send him out on loan for the rest of the season.
The severity of Nani's hamstring injury - still being assessed - could have a bearing on Moyes' decision, but either way Pulis has all-but written off Palace's chances of striking a deal.
He told talkSPORT: "We've spoken to David Moyes about Zaha and I don't think he's too keen on him coming back to London.
"It's not a problem for us, he's a Manchester United player. We don't think it's a goer, although we were very keen if there was a possibility to take him on."
While Palace appear set to miss out on one top target, Pulis is doing his best to bolster a side which has slipped back into the relegation places.
He said of his January transfer plans: "There are irons in other fires and we're working hard to bring other players in.
"It's what we need to do. I said when I came here that this window was important for Palace. If we can have a good window, then that gives us a better opportunity of staying up."