Coyle stated his interest in the 19-year-old over the weekend and has now revealed a formal offer has been lodged with the Championship side, but the Scot added that both clubs differ significantly in their valuations of the youngster.
Goal.com understands that Bolton have tabled a bid of around £5 million plus add-ons for Zaha as they look to reinvest the bulk of the money received from Gary Cahill’s transfer to Chelsea. Palace, however, are demanding at least £10m for their prized asset.
"I think it is documented now that we have made an offer [for Zaha], which we have," Coyle told reporters.
"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."
In addition to Zaha, Bolton are also thought to be looking to bring in another attacker on loan before Tuesday's transfer deadline, with Arsenal's Ryo Miyaichi and Porto's Juan Manuel Iturbe reportedly preferred targets.
Coyle refused to confirm interest in either player, but replied: "We are looking to bring a loan signing in as well and we do love exciting, young attacking players."
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