Skysports.com reports how the 19-year-old has attracted interest from a host of Barclays Premier League suitors after turning in a series of scintillating performances for the Eagles this season.
Reds boss Kenny Dalglish has been credited with an interest in Zaha as he looks to bolster his attacking options at Anfield this month, while Sir Alex Ferguson has been monitoring the player since he caught the eye against Manchester United in a Carling Cup clash at Old Trafford in November.
Both parties are yet to make an official approach for the talented England U19 international, who is expected to remain at Selhurst Park until the end of the current campaign.
With Palace eager to keep hold of Zaha, Coyle admits the likelihood of the Trotters engineering a deal is very slim.
"I think it is documented now that we have made an offer, which we have," he confirmed. "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."
Both Manchester United and Liverpool have much larger transfer budgets, and so would likely be able to offer closer to Palace's valuation of Zaha - so expect to see this transfer tug-of-war kick off again in the summer.