The 20-year-old's contract with Manchester City is due to expire at the end of June, and he is widely expected to return to Camp Nou on a free transfer despite interest from Arsenal and Paris Saint-Germain.
As it stands, Barca have still not agreed a deal with the centre-back, who has featured on 10 occasions for the Citizens during the 2020-21 campaign.
However, according to Sport, the Catalan giants are confident of securing a move for the Spain international before the end of April.
The report claims that Ronald Koeman's side recently had to readjust their contract offer to the youngster due to their ongoing financial problems.
Garcia, who initially left Barca in 2017, has hardly featured for Man City since making it clear that he would not be signing a new contract with the runaway Premier League leaders.