Koeman made no secret of his desire to sign the Netherlands international during the recent transfer window but a deal failed to materialise, despite the player agreeing personal terms.
The ex-Netherlands boss revealed earlier this month he remains hopeful of signing Depay, describing the attacker as a "great player" who can provide Barca with something different.
However, Garcia has not taken kindly to Koeman's comments over a player who remains under contract with the Ligue 1 side until the end of the campaign.
"Remind me to tackle Koeman when the moment is right," he said at a news conference on Friday ahead of Lyon's league trip to Lille this weekend.
"It's not the right moment yet, but when it is, I'll do it. We'll see what happens."
Barca have been tipped to make a fresh approach for Depay when the transfer window reopens in January.
He has been directly involved in eight Ligue 1 goals in eight outings this term - three more than any other player - and only team-mate Leo Dubois has created as many chances (24).
Since making his Ligue 1 debut in January 2017, meanwhile, only Paris Saint-Germain forward Kylian Mbappe has scored and assisted more times (108) than Depay's 83 goal involvements.
Asked if Depay will move on in a little over two months' time, Garcia said: "We'll have to wait and see how things go.
"He's not leaving for definite, but there will probably be clubs in for him soon."