The Serie A side have lined up a season-long loan deal with an option to buy the centre-back outright for £23m next summer.
Unai Emery is prepared to sanction Mustafi's departure having completed the £8m signing of David Luiz earlier this month.
Roma do not expect the player's wages to be an issue, with his current £2.75m salary in line with their own budgets.
Mustafi has largely struggled since joining Arsenal from Valencia for £35m in 2016.
However, the 27-year-old had an excellent two-season spell in Serie A with Sampdoria earlier in his career, and is thought to welcome the chance to return to Italy.
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