The 24-year-old played 45 games across all competitions for Barcelona last season and has started their first three La Liga matches so far.
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Barcelona came close to selling him before Flick took charge, but the German now sees the centre back as a key player.
According to Spanish outlet Sport, the La Liga champions have decided to reward his fine form with a new five-year contract.
The club were planning on doing so in the spring, but their ongoing financial issues forced them to delay talks with Garcia.