Record says Nunez, 22, was believed to be on Arsenal's radar in January with the club making initial contact with the player's agent.
The Gunners are increasing their contact with Benfica and are beginning to talk up a move to North London.
And Arsenal are reportedly a few steps ahead of Newcastle and West Ham in the race to sign Nunez.
Both clubs were said to be interested in the Uruguayan in January but were put off by his asking price.
At one point Toon were prepared to pay £50million for the forward but given interest in Nunez is only increasing his asking price is now believed to be in the region of £67m.
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