The midfielder's current deal is due to expire at the end of the season.
Tuttosport reports that Jorginho's agent are negotiating with Arsenal over a new contract.
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Jorginho's first choice is to stay at Arsenal beyond next season - but he also has other options on the table.
He and his representatives are in contact with several clubs in Serie A, including Juventus .
At the end of February, it emerged that Arsenal wants to extend the midfielder's deal - but it remains to be seen if the parties reach an agreement.