Former Bolton forward Coyle has emerged as Phil Gartside's first choice to help drag Bolton out of trouble and an official approach for the Scot, who rebuffed the advances of Celtic during the summer, now appears to be imminent.
Coyle initially appeared to distance himself from the job, although he described it as a "fantastic opportunity" but now appears willing to move, despite Burnley sitting above Bolton in the Premier League table.
Although there is still some way to go, and Bolton travel to Arsenal in midweek, the hierarchy at the Reebok Stadium hope to have a new man in place for the trip to Sunderland next Saturday.
Despite their perilous position, and the fact they did not really show it against Lincoln City, who sit 90th in the Football League pyramid, there is plenty to work with in the Bolton squad, although the new manger will be desperate to keep hold of defender Gary Cahill.
The first half was desperately poor, with Bolton enjoying all the possession without creating much at all but they secured their passage into the fourth round of the FA Cup with two quick goals at the start of the second period.
Matthew Taylor's cross flew in off the Lincoln defender Moses Swaibu and moments later, Ivan Klasnic burst into the area and crossed for Chung-Yong Lee to drill a second past former Tottenham goalkeeper Rob Burch.
Chris Herd, the on-loan Aston Villa midfielder, threatened Ali Al Habsi on several occasions from distance but the hosts wrapped the game up with seven minutes remaining, when Cahill rose to head in from a Mark Davies cross.
The Substitute Davies also added a fourth from close range in added time, touching in from Paul Robinson's cross.