The 34-year-old England international has been linked to a host of clubs - including Sunderland - after not starting in the Premier League since the defeat at Fulham on December 17.
Coyle has confirmed there have been no offers for Davies, who is out of contract at the end of the season, and insists he still has a role to play at the club, who face Swansea in the FA Cup fourth round on Saturday.
The Bolton boss told The Sun: "There's a lot of talk but the bottom line is I've not had an offer.
"I've spoken to Kevin and he knows he's a part of this club and we want him to stay here. Kevin will be the first to tell you he could have played better earlier in the season.
"If he'd played to the level he is capable of then he wouldn't have been out of the team - it's very simple.
"But he's shown in the last couple of weeks he's up for the fight and for me that's what I wanted to see."
Coyle wants his players who will be out of contract to show their desire to stay, adding: "I want players with a point to prove, ones who want to be at the club. All the power belongs to them.
"If they go out and play well, we want them to stay and other clubs will want them."
