Aston Villa are looking to strengthen their squad considerably in the January transfer window.
Debuchy has fallen out of favour at Arsenal this season, with Hector Bellerin establishing his place at right back.
There have been suggestions that the Frenchman could be set to depart the Emirates Stadium in January, and Garde has confirmed Villa’s interest.
"I had a conversation with Arsene Wenger two days ago about certain players, Debuchy was one of them,” he said.
“I am spending hours every day searching for players, I am looking for balance between English and foreign players but sometimes the price dictates this.”
Villa are eager to sign players in January, as they look to make an unlikely bid for survival.
The Claret and Blues are 11 points away from safety, and they have failed to win any of their last 19 Premier League matches.
Villa realise that they need to strengthen most areas of their squad, with a series of players linked with moves to the Midlands outfit.
Villa are also reportedly trying to sign Loic Remy from Chelsea, but Garde would not go into detail over whether there had been any progress with that deal.
"Last week I told you of my interest in Loic and I upset the Chelsea manager so today I will say nothing,” he added.