The Brazil international has emerged as a top target for the Gunners as they look to get value for money in the market.
Zaha is their ideal addition to strengthen their attacking options.
However, Crystal Palace are continuing to play hardball over a fee for the £80m-rated Premier League star.
Zaha has made it clear he wants to join his boyhood club, play European football and leave Selhurst Park this summer.
He has been away at the Africa Cup of Nations, but the Ivory Coast forward is finished with his international duty now.
While the 26-year-old is still intent on pushing through a move to the Emirates Stadium, Emery has reportedly turned his attention elsewhere now.
Having had a £40m bid – which is all what remains of their summer budget – rejected by Palace, Arsenal are looking to sign Everton instead.
The Gremio forward has been coveted by some of Europe’s top clubs.
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“Arsenal are now prepared to play close to £36m to seal a deal with Gremio”
And he shone as one of Brazil’s top performers at the Copa America this summer.
According to Spanish newspaper Marca, Arsenal are now prepared to play close to £36m to seal a deal with Gremio.
It is said the Gunners are closing in on the signing of the talented 23-year-old.
Everton himself has shown on his social media accounts recently how he has been studying English, adding fuel to the fire over speculation surrounding his future.
The player has also confirmed this week an offer has been made to him, although refused to name the club.
With Arsenal still trying to land £25m left-back Kieran Tierney from Celtic, they know they cannot blow their entire budget on a winger.
As a result, Everton would serve as a viable alternative to Zaha.
Elsewhere, a loan for Real Madrid midfielder Dani Ceballos is close to being confirmed.
A deal to sign William Saliba is also on the verge of being done, although Arsenal will only pay a fraction of the £27m up front for the centre-half as he will remain at Saint-Etienne on loan for the 2019/20 season.