Cole, 34, has failed to make an appearance for Roma this season after being frozen out by coach Rudi Garcia.
Villa, who are bottom after 15 games, will be looking to strengthen in January to avoid relegation for the first time in the Premier League era.
And Garde confirmed Villa are willing to offer Cole an exit route away the Italian capital.
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"Every good player is interesting for me and Ashley is a good player," Garde said. "He is someone who has experience but he didn’t play for a while now.
"Experience is also something we need. I will speak soon with the club and I’m already working on the January window. We know what we want to do.
"I feel we will need to improve the team to get more chances [to stay up]. For the moment, we have other games to play and to try to win, I am only focused completely on that."
Cole has plenty of Premier League experience, having made almost a combined 400 appearances for Arsenal and Chelsea.
Garde added: "We are seven points away from the safe zone and it’s many points, but so were Leicester [City] last season. If they can do it, then why can’t we?"