Official word is expected to come at a press conference scheduled for 11:45 EST.
Gauthier took over for Bob Gainey in February 2010, and served just over two years until today's decision.
This season, Gauthier's second full season at the helm, the Canadiens are dead last in the Eastern Conference with a paltry 29-34-14 record (72 points).
Montreal started the season losing its first three games on home ice for the first time in 74 years.
The Canadiens also changed coaches earlier this season, replacing Jacques Martin with interim head coach Randy Cunneyworth in mid-December, for which Gauthier and the franchise underwent severe criticism for Cunneyworth's inability to speak French fluently.
In 2010-11, Gauthier's first full season, the Canadiens finished sixth in the Eastern Conference, but lost in seven games to the eventual Stanley Cup champion Boston Bruins.
Overall, Gauthier's Canadiens compiled a record of 84-71-26 in the regular season during his tenure.
Gauthier spent nine years with Canadiens, originally joining the club as director of pro scouting in 2003.
No immediate replacement has been announced.
Ryan O'Leary is a writer and researcher for Bleacher Report's Video Production Department with seven years experience in the sports industry.