The French outfit are currently in talks with Brazilian side Fluminense about a possible move for the player, who signed a four-year deal with the Ligue 1 side in August 2012, but has since struggled to cement his place in the first team.
“He could be loaned to Fluminense. The two clubs are discussing,” the 46-year-old coach told Lyon’s official website.
A possible move to Brazil comes after the coach felt a mutual understanding with the player that things have not worked out for the best.
“Fabian has not necessarily brought what I was hoping for him and he probably wanted something else,” added Garde.
The Lyon trainer was also quick to clear up that if Monzon leaves the club, there will no replacement to fill the gap left by the 25-year-old.
He said: “If he leaves, he will not be replaced.”
The French giants currently sit second behind PSG in Ligue 1 on goal difference.