Mustafi has attracted interest from the likes of Inter and Juventus in recent weeks and is thought to be open to the idea of returning to Serie A, where he spent two years with Sampdoria earlier in his career.
Sky Sports News reports that Inter have now made a bid to initially bring Mustafi to the club on loan for a £4.6m fee, with the option to buy at the end of the season for £23m.
It is understood that the option to buy would become an obligation to buy should the Germany international feature in at least 50% of Inter's matches this season.
However, Arsenal are unwilling to sell Mustafi during the current transfer window, having already lost Gabriel Paulista to Valencia.
Mustafi made 26 Premier League appearances for the Gunners during his debut campaign at the club, but has only been involved in one of their three league games so far this term.