The midfielder is set to pen a new deal to 2027, says ESPN. The agreement will include a 12 month option.
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Brahim has won over new coach Xabi Alonso in preseason and is now happy to stay after weighing up his future towards the end of last term.
Indeed, Xabi held one-on-one talks with Brahim in recent days to help convince him about committing to a new agreement.
European champions PSG were in contact earlier this summer, but he is now set to continue his career with Real Madrid.