The midfielder has spent the season on loan in France and has confessed that he would like to stay, but it is unlikely that the reigning Ligue 1 champions can afford his wages
Earlier this week, the 30-year-old confirmed that he would prefer to stay with the French side rather than return to Anfield at the end of his loan spell.
And, whilst Garcia admitted that the club would like to retain Cole's services, he refused to reveal whether, as Goal.com understands, wages are proving to be a stumbling block to any proposed deal.
“It proves he is happy with us,” the Lille coach told reporters of the midfielder's comments on Friday. “We are happy with him.
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“There has been no debate on the reciprocal desires. But this is not the time [to talk].
“We have a big objective, so we don't waste our energy working on it [a permanent deal for Cole].
“What is certain is that everyone is under contract. There are special cases, and Joe is one because he is here on loan.”
Cole moved to Liverpool in the summer of 2010, after running down his contract at Chelsea, but had a tough season with the Reds, prompting his temporary departure to Ligue 1 12 months later.
He has so far made 45 appearances and scored five times in a Lille shirt.