Goal.com revealed in November that the Red Devils were keen on a move for the recently-capped England international, but are looking to strike a deal in the summer.
With the player himself also expressing his desire for a switch to the top flight, Arsenal have also been heavily linked with a move.
|9/4||Crystal Palace are 9/4 to be promoted with bet365
While Eagles chairman Steve Parish has said that he believes Zaha will "be a Palace player until the summer", the south London club's manager is drawing up plans for a return loan if he was to lose his star man this month.
When appearing on Sky Sports' the 'Footballer's Football Show' on Thursday, he was asked by its presenter: "So what's the plan for [Zaha] then? You get a big fee for him and get him back [on loan]?"
The former Blackpool boss replied: "You didn't have to be a genius to work that one out did you?"
While discussing the growing speculation on the show, the 49-year-old revealed that his chairman has spoken to "one or two clubs" regarding a deal but insisted he wants to keep Zaha to aid their push for promotion.
Reports suggest that the Red Devils could be open to loaning back the player, who made his senior England debut in a friendly against Sweden in November, should they secure his long-term services, however Palace's apparent £20m price tag could prove the stumbling block.