Davies has slipped out of Bolton's starting line-up in recent weeks after scoring just twice in the Premier League this season.
He is out of contract at the Reebok Stadium at the end of the campaign and Coyle has yet to decide on whether to hand his captain an extension.
The 34-year-old has been linked with moves to Premier League rivals Sunderland and Wolves before the close of the transfer window on Tuesday.
However, while admitting Sunderland counterpart Martin O'Neill has been in touch, Coyle says he has yet to receive any offers for Davies.
"The skipper got a wonderful reception because he is an outstanding player," said Coyle after Davies appeared as a substitute in Saturday's FA Cup win over Swansea.
"I can understand why there is interest in him.
"Martin rang me and I told him Kevin has a big part to play and I don't want him going anywhere. But you can't stop clubs enquiring, I do that myself.
"There is no offer. I think he loves the football club and he's shown that.
"He's been a credit to himself and us. But it's not easy when you are not in the starting line-up."
