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Ospina has spent the last four seasons at the Emirates Stadium but the Colombia international has never established himself as first choice with the Gunners.
The summer arrival of Bernd Leno has resulted in Ospina dropping further down the pecking order and according to The Mirror, Boca are looking to take advantage.
The Argentine club are allegedly prepared to pay in the region of £6m to sign the £29m, who still has two years remaining on his contract.
During his time in North London, Ospina has been restricted to just 70 appearances in all competitions.