The defender has also been closely linked with a move to Manchester United this summer.
Jose Fonte celebrates after scoring for Southampton
The defender has quietly turned into one of the bed defenders in the Premier League having come up with the Saints in 2012, and he was part of the Portugal side that won the European Championships in France this summer.
Portugal's Jose Fonte celebrates
That the 32-year-old has come into the international setup at such a late age but gone on to help his country to their ever title is testament to his qualities and especially his ability to provide an air of assurance to any back four he is in.
Nowhere could that be more welcome than at the Emirates, where Arsenal have found themselves decimated by injuries in central defence at the start of the season. Gabriel and Per Mertesacker are both out for several weeks, while Laurent Koscileny has been given an extended break after his European Championship exploits.
ESPN suggest both Arsenal and United have approached Southampton regarding the player, who would be available for around £10 million - significantly less than the London club's other chief defensive target.
Germany's Shkodran Mustafi and Italy's Simone Zaza in action
Germany international Shrokdan Mustafi has been closely linked to a move, but Valencia are said to be asking for £30 million (ESPN), more than Arsene Wenger would be prepared to spend. Whether that move progresses or not, the Gunners could certainly benefit from more than one addition, with question marks existing over the defence even before the injuries this summer.
Southampton fans would be desperately disappointed to see another star leave, especially someone who helped them since their days in League One. But after 267 appearances, if a significant transfer offer comes in for a player well into his thirties, the club may choose to consider it.
Frank Lampard in action with Southampton's Jose Fonte