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The Blaugrana are not particular well-stocked in central defence and only have Gerard Pique, Clément Lenglet and Ronald Araujo to play at the heart at the backline.
Dutch midfielder Frenkie De Jong has deputised on occasion but Barca are keen on bringing in another centre-back when the transfer window opens again in January.
According to Sport, German international Mustafi is one of a host of names on their shortlist. The former Valencia man refused a new contract at the Emirates and intends to leave the club upon the expiration of his current deal at the end of the 2020/21 campaign.
Barcelona could look to take advantage of the situation by attempting to strike a cheap deal for Mustafi in January as he looks to be the most realistic target.
The Catalan outfit remain keen on bringing academy product Eric Garcia back to the club after he turned down a contract extension at Manchester City, with the likes of Federico Fazio, Germán Pezzella and Mateo Musacchio also mooted as being on Barcelona's shortlist.
Mustafi started 15 of Arsenal's last 17 games under Mikel Arteta in last term's extended campaign before he had to undergo knee surgery in July.
Mustafi has made over 100 appearances for Arsenal since joining in a £35 million deal in 2016 but doesn't exactly have the best rapport with supporters.
One fan set up a petition calling for him to receive "life imprisonment" following some horrendous defending in a 3-1 defeat to Crystal Palace in 2019.
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