After it emerged at the weekend that Sunderland manager Martin O'Neill had made an enquiry about Davies, the Northern Irishman on Monday afternoon revealed that he has followed it up with a bid which has been rejected.
Coyle, speaking earlier in the day, had already stressed that he was not inviting offers for a player he insists remains very much in his plans.
As far as Coyle is concerned, Davies will still be with Bolton after the transfer window closes on Tuesday evening.
Coyle concedes, though, that things might be different if the 34-year-old - who is out of contract in the summer and has lost his place in the Wanderers first XI this season - indicates that he wants to leave.
"It (a bid) won't change my outlook," said Coyle, talking at a press conference this morning ahead of Wednesday's Premier League home clash with Arsenal.
"I want Kevin Davies here, regardless of what offer is made.
"The only thing that would change that circumstance is if Kevin Davies said to me: 'Gaffer, I think I want to look at that' - then that is different, because I have to understand Kevin's feelings on that.
"But he is our captain, he has been a huge part of Bolton Wanderers and he will continue to be.
"Of course, he is frustrated at not being in the starting line-up, because he has always been used to playing.
"He will be the first to tell you that, along with the rest of the group, his form has slightly dipped.
"But I saw enough on Saturday (when Davies came on as a substitute in the 2-1 FA Cup fourth-round win over Swansea) to see that he is up for the fight.
"He was terrific when he came on and showed how much the club means to him.
"I don't want him going anywhere and he knows that - I told him day after day last week, so he knows my feelings on it."
Bolton are pursuing transfer targets of their own and have made an offer to npower Championship outfit Crystal Palace for 19-year-old forward Wilfried Zaha - although Coyle emphasised that for the time being, it appeared 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 this month, 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 are reported to be on his radar - before tomorrow 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."
Ream, whose move was completed last week, is yet to make his Bolton debut and it seems unlikely he will get the chance to do so against the Gunners.
"He is having an appointment at the New York embassy today because after securing his work permit, he now needs to sort out his passport," Coyle said.
"The process starts today and I'm led to believe that it is a 48-hour turnaround, so I think Wednesday might be too tight for him - we'll just have to wait and see."
