Cole enjoyed a successful spell on loan at Lille last season before returning to Liverpool in the summer.
The 30-year-old has struggled to establish himself in Brendan Rodgers' plans this term and was criticised for his performance in last week's Capital One Cup defeat to Swansea.
Cole's long-term future has been the subject of speculation with the transfer window set to reopen in January and his former Lille team-mate Yohan Cabaye suggested over the weekend the former Chelsea and West Ham man should consider a return to the French club.
Garcia admits they could not afford to sign Cole on a permanent basis on the summer, but would love to bring him back to Lille.
"Joe is not only a great person, but also a great footballer. But financially it was not possible to save him," Garcia told RMC
"This can be prohibitive for the return of Joe to Lille. Sportingly and humanly, I'd love to see him back."