The idea follows a recommendation from new Argyle director Colin Sexstone, the former Bristol City chairman and chief executive who joined the Pilgrims' board recently.
Argyle owner and chairman James Brent said: "Colin was brought to the club for his extensive knowledge of the game.
"He has met with Carl Fletcher and, like the rest of the board, is very impressed with Carl's talent and enthusiasm.
"He has also identified - as we already knew - a lack of relative football experience across all areas of the club.
"The board, and Carl himself, feel the best way to address this area at first-team level is to appoint a director of football in a supportive role to the football management team."