According to a report from Goal earlier this week, Gumaraes emerged as a possible target this summer for the Gunners, with Mikel Arteta wanting to add to his options in the middle of the park.
However, while Arsenal are willing to pay around £25 million for the Brazilian, a report from Globo.com has stated that Lyon have put a higher price tag on him, with them demanding closer to £34 million if they are to sell him this summer.
Guimaraes has a contract with the French club until June 2024, yet they could be enticed to sell him if the right offer for him is made.
The 23-year-old is the latest name added to Arsenal's possible targets for central midfield, with the likes of Yves Bissouma, Sander Berge and James Maddison all being linked with the club, but no deals have been agreed so far.
Albert Sambi Lokonga remains the only midfielder that the club has signed so far this summer, with the Belgian joining from Anderlecht for a reported £15 million plus add-ons.
With the Gunners recently splashing the cash to sign Ben White, it remains to be seen whether they will be willing to pay so much for Guimaraes, and a deal is probably also dependent on the future of Granit Xhaka, with his move to AS Roma being on standby.
Guimaraes is currently away on international duty at the Tokyo Olympics with Brazil, where he has played in three games so far in defensive midfield, providing two assists in the process.
The Brazilian made 37 appearances in all competitions for Lyon last season, even contributing to the attack with three goals and one assist, as Lyon finished fourth in Ligue 1.