The Catalan giants are keen to sign the centre-back, but have so far refused to meet Manchester City’s €20m asking price, with their latest bid touching €15m.
Garcia is in the final year of his contract at Manchester City and will not put pen to paper to a fresh deal as he wants to return to former club Barcelona.
The clock is now ticking down on the transfer window and, according to Spanish radio station RAC1, Barcelona are now holding talks with Manchester City.
They are trying to thrash out a compromise with Pep Guardiola’s side.
It remains to be seen if they will be able to do so.
Manchester City are happy to keep hold of Garcia until the end of his contract if Barcelona do not offer an acceptable deal.
The Catalan giants are suffering financial difficulties and are counting on the departure of Jean-Clair Todibo to Benfica to help fund a deal for Garcia.