Torreira is Arsenal's main central midfield target and they are hoping to reach an agreement on a deal for the Uruguay worldwide, who has a €25 million release clause.
Lucas Torreira is now in Russian Federation preparing for the World Cup with Uruguay.
According to the same story, the Uruguayan has a €25m (£22m) release clause in his contract with the Italian club, but the Serie A side have asked Arsenal to pay €30m and instead spread the payments out over several years.
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It is already looking like it will be a big summer for the Gunners, with Unai Emery having taken on the challenge of replacing Arsene Wenger, who held his post for 22 years, although had let the squad diminish into a team of average players.
Arsenal transfer target Bernd Leno has invited rumours linking him with a move to north London by "liking" a post on Instagram suggesting he is the club's No.1 candidate.
That could suit Arsenal, given that the Gunners are understood to have a more restricted transfer budget this summer following their lack of Champions League football.