The Kings, who are averaging just 2.21 goals per game, are 12th in the Western Conference with a 13-12-4 record.
After two straight playoff appearances and the acquisition of former Flyers captain Mike Richards in the offseason, expectations were elevated for the 2011-12 campaign.
Murray, 61, took over behind the Los Angeles bench for the 2008-09 season in place of Marc Crawford, and compiled a 139-106-30 mark during his tenure with the Kings. He also has held head coaching positions with Washington (1990-94), Philadelphia (1994-97) and Florida (1998-2001).
The 45-year-old Stevens is in his second season with the franchise.
Prior to joining the Kings, Stevens posted a 120-109-34 record while serving as the Flyers head coach from 2006-2009. Philadelphia reached the Eastern Conference Finals in 2008 under Stevens, who won a Calder Cup championship in 2005 as the head coach of the Flyers' AHL affiliate, the Philadelphia Phantoms.