Gomes has struggled to make an impact on the first team at Barcelona and has regularly faced criticism from supporters who believe that the 24-year-old is simply not good enough for the team.
The report comes from French outlet Paris United, who wrote: "Arsenal have opened talks with Andre Gomes. FC Barcelona will not keep him."
The Portuguese midfielder has been subject to transfer rumours for a while, with his name linked to the likes of Tottenham and Chelsea. However, Sport have reported that Arsenal and Juventus are the two teams with the most interest in Gomes.
Sport claim: "At the moment, there are two clubs who appear to tick all the boxes: Arsenal and Juventus. "
"They still need to agree on a fee though, with Barcelona valuing him at €20m. However, neither Juve nor Arsenal are willing to pay that much and the most likely scenario is reaching a compromise of around €18m."
The report states that Gomes will not travel with the Barcelona squad for their pre-season, in order to secure a permanent transfer away.
Their valuation of around £18m would leave the club making a loss on Gomes, who they signed from Valencia for around £33m in 2016. Barcelona are keen to recuperate as much of their initial fee as possible, with Sport claiming that the Catalan giants are insisting on a clause which would gift them a percentage of any future transfer which Gomes may make.
Last season, Gomes made 31 appearances for Barcelona, but only started 12 of those matches. Furthermore, he only completed 90 minutes in six of those appearances. He managed to register one assist in his 31 appearances, and it appears as though Barcelona are unconvinced by Gomes.
Arsenal already have multiple options in the centre of midfield, including new signing Lucas Torreira, but it remains to be seen how Emery will incorporate all these midfielders, or whether he will look to sell some to make space for Gomes.