Cole has returned to Liverpool after spending the 2011/12 campaign with the Ligue 1 side.
But Garcia is keen to strike a deal with whoever succeeds Kenny Dalglish at Anfield for the midfielder, who scored four goals in 27 appearance.
"From a sporting angle we would like to keep him," said Garcia, who is resigned to losing his Belgian playmaker Eden Hazard.
"But he does not belong to us and he has not discussed matters with Liverpool.
"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."
Cole joined Liverpool on a four year contract in 2010 on a free transfer from Chelsea but failed to impress in his first season and was sent out on loan by then-manager Dalglish.