Burnley chairman Barry Kilby said: "The backroom staff will take the team on Saturday and Steve will be in charge."
Lawyers from both clubs are currently working on a compensation deal for Coyle, who has expressed a wish to leave Turf Moor.
Kilby has also voiced his discontent with Bolton in their pursuit of Coyle. He said: "I don't think we are best of pals at the moment. It was an unwelcome approach.
"Owen felt Bolton do have a larger player budget than we have and it was his best way of remaining a Premiership manager, working with a budget of that size.
"It's been a trauma for the football club. None of us wanted Owen to go. It was a shock when all this broke. We are all grown men and know how football works but it was quite emotional when Owen left.
"I fully expected when he did move it would be upwards, not sideways to a club we are fighting a relegation scrap with. We were surprised.
"But I have been in football long enough to know these things happen and I don't think Owen took this decision lightly.
"It was with regret that he went and he did say to me there was only Celtic or Bolton he would leave Burnley for. But it has come at a bad time, that is for sure."
Davis will take the reins against Stoke with the help of goalkeeping coach Phil Hughes.
Kilby confirmed: "The backroom staff will take the team for Saturday and Steve will be in charge."
Kilby is now keen to find a replacement for Coyle sooner rather than later.
He added: "We have got to get going. Let's put this behind us and make sure we stay in this Premier League.
"We have to see who is out there. We need to get this one sorted out as soon as we can."
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