The Germany international is out of favour as the French champions begin a new era under former Borussia Dortmund coach Thomas Tuchel.
Radio Sevilla declared talks have already taken place between the two clubs for the 24-year-old, who was a member of Germany’s World Cup finals squad in Russia last summer.
Draxler featured in two games during the woeful campaign which saw the 2014 World Cup winners exit at the group stage.
Arsenal are long-time admirers of the former Wolfsburg and Schalke starlet, whose transfer dealings have been a series of left-field moves. Joining Wolfsburg threw a curveball into his career but a £34m move to PSG in January 2017 seemed to take him into the big time.
The move hasn’t worked out and with former PSG head coach Unai Emery now in charge at the Emirates, a move to the Premier League seems unlikely.
Despite reaching the Europa League places, Sevilla weren’t a free-scoring side last season with Wissa’m Ben Yedder their top goalscorer with nine in La Liga. The Andalusians hope he will rediscover his form of 2012-13 when he netted 11 for Schalke.