Mustafi's contract with Arsenal ends in June, and he is not expected to sign a new contract at the club.
The German centre-back has barely played this season, playing just 44 minutes of Premier League football across two appearances, whilst also playing twice in the UEFA Europa League.
Summer signing Gabriel Magalhaes, along with David Luiz and Rob Holding, have all been picked ahead of him in the team so far this season.
Mustafi was linked with a potential move away from Arsenal during the summer, with several European clubs interested in signing him, mainly from Italy.
He has also reportedly turned down a new contract at the Emirates, and as a result, he has now emerged as a possible short-term option for Barcelona.
Ronald Koeman has plenty of defensive problems, with the only real options to choose from being Gerard Pique, Clement Lenglet, Samuel Umtiti and Ronald Araujo, with all of them having their own individual difficulties such as injuries, inconsistency and with the latter, inexperience.
Barcelona's main target is 19-year-old Eric Garcia from Manchester City, who is an academy product of Barcelona, but City are holding firmly to him, wanting him to either go for a big transfer fee or else to sign a new contract at the club.
Speaking on Mustafi's future, his father said "Nothing is ruled out, we can imagine everything, because Shkodran is [available on a] free transfer in the summer."
The 28-year-old had a resurgence last season under Arteta, featuing in seven of the ten league games after the restart.