The south Londoners beat Watford 1-0 in the Championship play-off final on Monday. The 20-year-old Zaha won the spot-kick that sealed victory in what was meant to be his final Palace game before joining champions United.
"They might want him to get experience in the Premier League playing for us rather than maybe not playing for them. I don't know, of course," Palace co-chairman Martin Long was quoted as saying by Sky Sports on Tuesday.
"We probably will ask."
New United boss David Moyes, who will inherit a stellar squad from the retired Sir Alex Ferguson when he takes charge next season, must weigh up whether Zaha will get enough game time in competition with the likes of Ashley Young and Antonio Valencia.
Palace manager Ian Holloway, who spent a season in the top flight with Blackpool in 2010/11, has not given up hope of keeping his best player despite Zaha's 15 million pound transfer.
"I think he [Moyes] would be silly to give me him back. Now we're up it might be realistic, but who knows?" he told reporters after Kevin Phillips' extra-time winner, which could earn Palace as much as 120 million pounds in top-flight income.
Palace, rescued from administration three years ago after a group of local businessmen took over, return to the top flight after an eight-year absence and join Cardiff City and Hull City, who won automatic promotion from the Championship.
Zaha made his England debut as a substitute in the 4-2 friendly defeat by Sweden in November, only the second Championship outfield player in five years to be called up by England.
