The Gunners are hoping to secure the 21-year-old in a deal that could cost up to £8.5million.
Tavares is currently in quarantine in the UK, per the government's COVID-19 guidelines.
Arsenal hope that Tavares will be signed and sealed in time for him to take part in preseason training with his teammates.
The Gunners are also busy moving players out of the club, with midfielder Matteo Guendouzi close to securing his departure to Marseille.
Guendouzi will sign on an initial loan with a view to a permanent deal for roughly £10 million next summer.
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