Mustafi endured a difficult time last season and has become a scapegoat among suporters for the Gunners’ defensive problems.
The German, 27, is a World Cup winner but has struggled to adapt to life in the Premier League since he was signed by former manager Arsene Wenger from Valencia in a £35million deal in 2016.
The likes of Monaco and AC Milan have been linked with a move but Arsenal are yet to receive any formal offers.
However, with foreign clubs the only potential suitors for Mustafi, the Gunners are under little pressure to rush a deal through because the transfer windows around Europe will remain open after Thursday’s 5pm deadline in England.
Teams in La Liga, Serie A, the Bundesliga and Ligue 1 can continue to sign players until September 2 while English clubs are also able to sell beyond the close of their own window.
BBC sports report David Ornstein says that gives the Gunners more time to find a new home for the unwanted player but insists the player himself is keen to stay at the Emirates.
He also claimed Arsenal are considering a loan move for striker Eddie Nketiah with Bristol City said to be keen to take him.
“Highly-rated 20yo striker Eddie Nketiah set to leave Arsenal on season-long loan,” Ornstein wrote on Twitter.
“Bristol City among a number of clubs in talks to sign England youth int’l.
“Currently no firm offers for defender Shkodran Mustafi & he wants to stay – but foreign teams have longer to do a deal.”
Arsenal appear to be already working on a deal to bring in a replacement for Mustafi who was first choice for most of last season despite his poor form.
Manager Unai Emery is reportedly keen to sign RB Leipzig defender Dayot Upamecano, 20, with the German side looking for a fee of around £70m.
Emery still waist a new left-back as well and still bring in Kieran Tierney, 22, from Celtic before the deadline.
Meanwhile, Laurent Koscielny, 33, is currently in talks with Rennes over a potential return to France.