The Glasgow-born boss has left Turf Moor after expressing a wish to join Bolton, where he had a spell as a player in the 1990s.
Coyle led Burnley into the top flight for the first time in 33 years after moving from St Johnstone in November 2007.
But he believes Bolton is a better option and is poised to replace Gary Megson at the Reebok Stadium.
Evans marked his first match at the helm with a victory last weekend when Lincoln were beaten 4-0 in the FA Cup.
Bolton were due to face Arsenal at the Emirates Stadium on Wednesday night but that match was postponed due to the weather.
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