Blackburn announced that they have released Appleton and his assistant, Ashley Westwood, from their duties on Tuesday morning, leading to immediate speculation that Murphy could be involved in the coaching shake-up.
Murphy was stripped of the club captaincy last week after some poor displays and, although he does not have the requisite coaching badges to take a full-time managerial appointment, he could be installed in a caretaker role until the end of the season.
The 36-year-old ex-England midfielder was linked to a coaching role at his former club Fulham, but any departure from the club is complicated by his two-year, £40,000-a-week deal at Rovers.
First-team coach Darren Moore and head of senior recruitment Luke Dowling have also gone in the cull.
Blackburn last week