After it emerged at the weekend that Sunderland manager Martin O'Neill had made an enquiry about Davies, the Northern Irishman on Monday revealed that he has followed it up with a bid which has been rejected.
Coyle conceded the 34-year-old - who is out of contract in the summer and has lost his place in the Wanderers first XI this season - could go if he indicates that he wants to leave, but said: "It (a bid) won't change my outlook."
Coyle, talking at a press conference on Monday ahead of Wednesday's Barclays Premier League home clash with Arsenal, added: "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."