The News of the World says Megson is fighting for his future after failing to win over his critics, who have targeted him since he first arrived. He was forced to apologise for branding some of the Wanderers' supporters "pathetic" earlier this month.
Now plans are afoot to oust the former West Brom and Leicester boss in the summer and replace him with Coyle, who has worked wonders at nearby Burnley.
Coyle was a leading candidate to take the Bolton job from Sammy Lee in October 2007 but his inexperience ultimately counted against him and he moved to Burnley a month later. However, his impressive results at Turf Moor have made some members of the Bolton board take note.