The movie, which Coppolla wrote and is directing and producing, is about a famous graphic designer who plummets into a vortex of despair after his girlfriend dumps him.
Youree Henley also is producing.
Coppola is the son of Francis Ford Coppola and the brother of Sofia Coppola — who directed Murray in her 1993 "Lost in Translation."
Roman Coppola was nominated for a BAFTA Award for best special effects for the 1992 "Dracula."
Murray also stars as Franklin D. Roosevelt in the upcoming "Hyde Park on the Hudson," now in post production, and in "Moonrise Kingdom," also in post production.
"A Glimpse Into the Mind of Charles Swan III" is set for a 2012 release.