The Portugal international has failed to establish himself at Barcelona since arriving in 2016, and could be booted from the club this summer to make room for new signings.
Gomes would be a surprise target for Emery, but the Arsenal boss is a massive admirer and thinks he can reignite the 24-year-olds form and confidence.
The Independent claim Emery is so keen on Gomes, he is ready to sacrifice several Arsenal stars to raise the transfer funds.
Arsenals transfer kitty is almost empty after the additions of Bernd Leno, Stefan Lichtsteiner and Sokratis Papastathopoulos.
Once Arsenal complete the signing of Sampdoria midfielder Lucas Torreira, Emery will have spent the entirety of his budget and will need to sell to continue spending.
Emery is prepared to do just that to land Gomes, who will cost around £30million.
Centre-back Calum Chambers has been given a new contract, but there are doubts about the futures of Shkodran Mustafi, Petr Cech, David Ospina and Lucas Perez.
The sale of Mustafi and Perez could raise the necessary funds to bid for Gomes, as Emery sets his sights on firming up a fragile midfield.
Gomes is under contract at Barcelona until 2021, meaning Barcelona can name their price for the Portuguese.
Emery has been linked with several raids on La Liga this summer, with the Gunners said to be exploring the possibilities of signing Sevilla duo Ever Banega and Steven NZonzi.
Interest in NZonzi has been ongoing for several months, while Banega is a favourite of Emerys having worked under the Spaniard at Sevilla and Valencia.