Coyle spoke over the weekend about his interest in the 19-year-old and revealed on Monday morning that a bid for Zaha had been lodged with npower Championship side Palace - but also indicated that for the time being, the two clubs were not in agreement over the player's valuation.
"I think it is documented now that we have made an offer, which we have," Coyle said.
"I don't think it is to the value that the Crystal Palace chairman (wants), but it is an offer we felt was fair for where a very talented young player is at the moment.
"I always put what I think is a fair value on a player and if we get to it, great.
"If we don't, then we have to accept that we are not going to pay what we would believe would be over the odds.
"But he is such a talented young player and he will get better - there is scope for improvement. He has got pace and unbelievable quality and natural attributes.
"We would love for that to come to fruition, but at the moment it looks as if we are a way apart in terms of valuation."
Coyle, who has already recruited United States defender Tim Ream from the New York Red Bulls during the current transfer window, is hoping to wrap up the signing of Zaha as well as a loan deal for another attacker - Porto's Argentinian 18-year-old Juan Manuel Iturbe and Arsenal's Japanese 19-year-old Ryo Miyaichi being reported targets - before Tuesday night's deadline.
When asked about Iturbe and Miyaichi, the Wanderers manager said: "We are looking to bring a loan signing in as well and we do love exciting, young attacking players."