The 30-year-old has returned to Liverpool after a season on loan at the 2011 Ligue 1 champions where he scored four times in 27 appearances and Garcia admitted he would be interested in having him back.
"From a sporting angle we would like to keep him," said Garcia, who is resigned to losing his Belgian playmaker Eden Hazard in a multi-million euro deal during the summer.
"But he does not belong to us and he has not discussed matters with Liverpool," he said. "It is a very fluid situation. The only certainty for the moment is that he is returning to Liverpool, the club to which he belongs."
Should Cole return to Lille he would have UEFA Champions League football to look forward to, as they finished third in Ligue 1 last season, whereas Liverpool finished eighth and have only a Europa League campaign ahead of them owing to their success in the League Cup.
Cole joined Liverpool on a four year contract in 2010 on a free transfer from Chelsea, but he failed to impress in his first season and was sent out on loan by then manager Kenny Dalglish at the beginning of last term.