Mari went on loan to the Italian club in January and played 15 Serie A matches for them, missing only the occasional game.
His performances were good enough that they convinced Udinese to pursue a permanent deal for the centre-back in the approaching transfer window.
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The Italian club have decided to part ways with caretaker boss Gabriele Cioffi, after the side finished 12th in the Serie A table.
Cioffi’s exit has had the knock-on effect of plunging into doubt the Gunners centre-back’s permanent transfer to Udinese.
The interim boss was crucial in bringing in the centre-back on loan in the first place to Italy and his sacking could mean Mari heads back to London.
The matter could still be resolved if the Italian team appoint a new coach and pursue Mari, though there is uncertainty over how much they would be able to pay to make his signing permanent, the Gunners having brought him for £14m and wanting to recoup as much as they can from his sale.
The Gunners have established centre-backs at the Emirates, to whom could be added William Saliba in the summer, and thus Mari might find opportunities limited next season if he does not leave.