Arthur returned from Brazil last week after going AWOL from the club's Champions League campaign. The midfielder walked out after failing to see any action since the season restart.
Arthur has now signed for Juventus and wants Barca to release his registration.
The player met with Abidal to explain his position and the sporting director will now meet with coach Quique Setien to discuss whether Arthur should be allowed to rejoin training.
Arthur has been sold to Juve for €72m plus €10m in bonuses.
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