The report suggests Manchester United are keen to strike a deal allowing Zaha to stay at Palace until the end of the season, before completing his move to Old Trafford in the summer.
The 20-year-old has been monitored by a number of Premier League clubs, including Tottenham, Liverpool, Manchester City and Arsenal, and is likely to be one of the most in-demand players in January.
Arsenal chief scout Steve Rowley is a huge admirer of Zaha after watching him on several occasions, and Zaha is thought to be an Arsenal fan.
But Manchester United are ready to strike first for the England under-21 international after a series of stunning performances for Palace, who currently sit top of the Championship table.
Zaha's form has earned a call-up to Roy Hodgson's England squad, and the young winger is expected to make his debut against Sweden this evening.
The report also suggests Ferguson could be eager to sign Zaha as a direct replacement for Nani, who has less than a year left on his United contract. His Old Trafford future appears to be under threat, and the Portuguese star has been linked with a move away from United.
Zaha is under contract at Selhurst Park until 2017, so Palace are in no rush to sell, and the club co-chairman Steve Parish has indicated a bid of at least £20m will be needed to lure the youngster away from south London.
But with Liverpool, Spurs, City and Arsenal all interested the bidding is expected to start around £10m, although it's likely to ratchet up quickly with so many interested parties.
The recent England call-up is reward for Zaha's emergence this season, and the youngster is widely regarded to be the best player in the Championship. Still just 20-years-old, Zaha has already made 107 appearance for the Eagles since making his first-team debut aged 17.
Scouts from Arsenal, Liverpool, Spurs, United and City have competed for space on the Selhurst Park terraces as they each weigh up Zaha, but so far no bids have been forthcoming, at least officially.
That's expected to change in January when the transfer window reopens, and the report suggests Manchester United will be looking to get ahead of the pack.