Spanish media outlet Sport, as quoted by the Daily Mirror, is reporting that the Gunners are interested in a deal to sign the Portugal international this summer.
The same article states that Arsenal are facing competition from Tottenham Hotspur in the race to sign the attacking midfielder from the Catalan side.
According to the same story, the La Liga champions have deemed Gomes surplus to requirements at FC Barcelona this summer.
Gomes moved to FC Barcelona in a €35m plus a further €20m in add-ons from their La Liga rivals Valencia in the 2016 summer transfer window.
The 23-year-old has scored three times in 78 games in La Liga over the past two seasons following his impressive stint at los Che.
Arsenal finished in sixth place in the Premier League table last term to culminate in Arsene Wenger’s dismissal as Gunners boss.
The Gunners started their summer spending under new manager Unai Emery with the addition of veteran Juventus and Switzerland defender Stephan Lichtsteiner.
Emery completed deals to sign Borussia Dortmund defender Sokratis Papastathopoulos, Bayer Leverkusen goalkeeper Bernd Leno and Sampdoria midfielder Lucas Torreira.
Teenager Matteo Guendouzi completed a switch to Arsenal from Lorient last week.
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