The 20-year-old has been expected to complete a move back to Catalonia ever since Pep Guardiola revealed that he had turned down the club's offer of a new contract.
However, cash-strapped Barcelona supposedly want to wait until the summer to complete a deal for Garcia - who will be a free agent by that time - although that decision could leave the door open for other clubs to steal a march in the race for the Spaniard.
According to Mundo Deportivo, PSG are keen admirers of the Manchester City man and are planning to swoop if Barca cannot agree a deal.
The report claims that Barcelona remain confident about their chances of winning the race, but Garcia is not ruling out a move to the French capital just yet.
The centre-back's game time in the 2020-21 campaign has been hampered by injury and a positive coronavirus test, and he has only made three Premier League appearances all season.