The Daily Express says the Gunners are set to splash the cash as Mikel Arteta desperately looks to bolster his attack.
And Arsenal have entered into negotiations with Nunez's representative.
They add that the 22-year-old fits the recruitment team's policy of continuing to sign players under the age of 24.
Arteta wants a dynamic striker capable of getting behind defences as well as playing with his back to goal at the tip of his preferred 4-3-3 formation.
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