Sunderland boss Martin O'Neill made an enquiry about the availability of Davies, 34, at the weekend, but Coyle informed his managerial counterpart the forward is part of his plans at the Reebok Stadium.
O'Neill has since lodged an official bid ahead of the close of the transfer window on Tuesday night, and the Trotters have rejected the approach, despite the Trotters skipper's current contract being up for renewal in the summer.
"When Martin rang last week it was just an enquiry," Coyle said on Monday. "There was no offer made. He wanted to know the situation and I told him quite clearly, I didn't want Kevin Davies going anywhere.
"I'm not encouraging anything for Kevin Davies, because we want him here as the captain. It (a bid) won't change my outlook. 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."