Roma manager Jose Mourinho has identified the 28-year-old playmaker as a potential target ahead of the new season.
According to Sky Sports News, Arsenal value the Swiss international at around £21.5m, however, the Italian outfit are only willing to pay up to £10m plus bonuses.
Xhaka came close to leaving the Gunners and joining German club Hertha Berlin in January 2020, however, the attacker decided to stay in north London.
Arsenal boss Mikel Arteta would consider letting Xhaka leave this summer, as the Premier League giants are looking to obtain funds from player sales to recruit new additions.
Xhaka racked up 220 appearances for Arsenal during a five-year spell, including 45 outings in all competitions this term.