The Clarets launched a desperate bid to keep the promising young manager at Turf Moor but he has informed his employers he wants to move across Lancashire to replace Gary Megson.
Coyle has "reaffirmed his desire to leave Burnley", the club said in another statement and talks will now take place in a bid to thrash out a compensation package.
Bolton chairman Phil Gartside is close to landing his man after considering Coyle as an option before plumping for Gary Megson in 2007.
Megson was never popular with the Reebok faithful and was axed after a 2-2 draw with Hull last month.
Coyle represented the Trotters as a player and will have a bigger budget to work with at his new club.
The exit is a massive blow to Burnley and their chances of avoiding relegation, as they have been punching above their weight this term on the back of some outstanding home form.
Clarets chairman Barry Kilby has confirmed coach Steve Davis will take temporary charge for Saturday's clash with Stoke.
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