That means the Clarets are searching for a manager capable of keeping the team in the Premier League.
Chairman Barry Kilby and operational director Brendan Flood have already begun their search for the 43-year-old's successor, with several bookmakers making Norwich boss Paul Lambert an odds-on favourite for the post on Thursday.
Among the criteria Burnley will look for will be an inclination to keep playing attractive football, which has epitomised the club's rise from the Championship to the top flight.
Flood told his club's official website: "The culture of the club is very strong so we have to make the right decision to get somebody who fits that culture and I'm sure if we make that decision the players will warm to whoever we choose.
"We don't want somebody who is significantly different but we want someone who might add some value and improve the club.
"We have all fallen in love with the way we play again so I think we've got to try and find somebody who's going to keep that recipe going so that we can entertain the fans."
Burnley and Bolton remain locked in negotiations over a suitable compensation package for Coyle, who still had three-and-a-half years left on his contract at Turf Moor before declaring his desire to move to the Reebok Stadium.
Steve Davis and Phil Hughes are ready to lead the Clarets in Saturday's match against Stoke with Coyle on 'gardening leave'.
Sam Allardyce believes Burnley should have "broken the bank" to try to keep the Scot at Turf Moor.
Asked if he thought Coyle would be successful at the Reebok Stadium, Blackburn boss Allardyce said: "Yes, I'm sure he will. I think it's a big loss for Burnley.
"They should have broken the bank to keep him because he has shown to be single-handedly, the key, most important person at Burnley for many, many years.
"They should have gone a lot farther to try and keep him.
"Bolton have got themselves a very good young manager if that gets sorted out over the next few days."
Meanwhile, Swansea boss Paulo Sousa admits he is flattered to hear his name linked to the vacant managerial position at Burnley.
The former QPR boss explained: "My ambition is to grow and I have said I want to go to the Premier League, of course.
"I am proud to be linked to Burnley. It is very important for me and for everyone to be recognised and it means we (Swansea) are doing well once more."
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