The Frenchman is currently suffering with a mini injury crisis in north London, with the absences of players such as Jack Wilshere, Aaron Ramsey and Alex Oxlade-Chamberlain having limited his central options.
And reports claim that Wenger is eager to address this issue in January with a move for Jorginho.
Gunners scouts travelled to Italy to watch the 23-year-old in action against Genoa on Sunday, hinting that their interest in the Brazilian is strong.
Liverpool have also been aligned with the ex-Hellas Verona man since the arrival of Jurgen Klopp, but Arsenal’s current status as genuine Premier League title contenders may appeal to the player.
Jorginho is most comfortable in a central midfield position, but can be used as a playmaker or in an anchoring role.