According to the Mirror report, citing sources at UK Sun, the 29-year-old has been linked with a move to the Emirates' in recent transfers and is now looking likely that N'Nonzi will finally return to the English topflight this summer.
England worldwide defender Calum Chambers is willing to battle to gain a first choice place at Arsenal after signing a long term contract on Tuesday.
Should the Frenchman and Torreira arrive to provide competition for the likes of Granit Xhaka, Aaron Ramsey and Mohamed Elneny, Arsenal would be looking in good shape in central midfield ahead of a crucial 2018-19 season.
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"The World Cup is important and being part of this squad meant a lot to me".
Calum Chambers has signed a contract extension at Arsenal, with new head coach Unai Emery saying Englishman remains part of his plans at the Emirates.
"I've met some great people here and I'm really excited about the future and I want to kick on and prove to everyone the player I can be".
Torreira has a (€25m) £22.1m release clause in his Sampdoria contract but the Gunners have made a decision to pay a premium so they can spread out the payments.