The 30-year-old moved to Liverpool on a free transfer from Chelsea in 2010 but failed to make an impact under ex-Liverpool bosses Roy Hodgson and Kenny Dalglish, resulting in a temporary move to France last September.
The former West Ham United youth graduate scored nine goals in 42 appearances for the 2011 Ligue 1 champions, and Garcia is eager to retain Cole’s services, with Lille star Eden Hazard set to quit the club and move to the Premier League this summer.
“From a sporting angle we would like to keep him,” said Garcia. “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.”
In April, Cole stated his desire to remain at Lille after a promising first season in the French league.
“It’s something I would like to do [extend stay at Lille],” said Cole.
“It’s not in my hands at the moment but I’m very happy here, my family is very happy here.
“We have to wait to see where Lille finish in the league and then start planning for next season.”
Cole, who has been capped 65 times by England, signed a four-year deal with Liverpool in June 2010.
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