The 29-year-old French midfielder has been identified by the Italian side as a possible upgrade on Maxime Gonalons, who looks likely to move to Crystal Palace according to Calciomercato.
N'Zonzi has been widely expected to leave Sevilla for some time with his release clause of £36m unlikely to be an obstacle for Europe's top clubs.
However, despite reports of Roma being close to a deal, the Champions League semi-finalists are not believed to be looking to pay N'Zonzi's fee in full.
New Arsenal boss Unai Emery knows N'Zonzi well, having previously managed Sevilla between 2013 and 2016 - where he won three consecutive Europa League titles. N'Zonzi joined the Spanish club in 2015, winning the last of those European trophies that came under Emery's reign.
The defensive-minded central midfielder has even greater silverware in his collection now too, having won the World Cup this summer with France.
N'Zonzi has made nine senior international appearances since making his debut for the national team in November 2017, in a friendly win over Wales.
The 29-year-old has made a total of 136 appearances in all competitions, and netted eight goals, during his time in La Liga with Sevilla.
N'Zonzi has had a strange rise to the top in terms of his career so far, having previously called Blackburn Rovers and then Stoke City home, prior to making the reported £7m move to southern Spain in 2016.