United are thought to be leading the chase for Zaha and they are expected to firm up their interest with a bid for the skilful winger this week.
Arsenal have also been long-term admirers of Zaha and they are ready to rival United for the 20-year-old.
Zaha is regarded as one of the best young talents outside the Premier League and he made his England debut earlier this season.
Zaha has already stated his desire to play in the top flight and Crystal Palace are reluctantly willing to sell him for the right price.
Eagles boss Ian Holloway revealed over the weekend any deal for Zaha must include the provision for the winger to return to Selhurst Park for the rest of the season.