The 20-year-old has been the subject of long-term interest from numerous Premier League clubs, following a series of stand-out performances in the Championship over the past 18 months.
Red Devils boss Sir Alex Ferguson is believed to have held talks with Palace, and are confident of securing a deal after proposing a package worth up to £12million, even though Eagles chairman Steve Parish put an initial £20million valuation on Zaha's head.
Arsenal have also been in the running for the England international, but Arsene Wenger's interest is thought to have now cooled, given their reluctance to get into a bidding war with Manchester United, and with Theo Walcott set to sign a new contract with the Gunners, and stay at the Emirates Stadium.
Manchester United are understood to be open to the idea of loaning Zaha back to Palace for the rest of the season, something manager Ian Holloway will be keen to ensure as his side continue their push for promotion.
The Premier League leaders agreed a similar deal for Chris Smalling in January 2010, allowing the defender to remain at Fulham until the end of that season.
Zaha's arrival at Old Trafford would inevitably lead to questions about Nani's future, but Ferguson insisted recently that he was hopeful the unsettled Portugal winger would sign an extension to his present contract, which expires in 18 months.