Torreira - who is now with the Uruguay squad preparing for the World Cup - is reportedly Emery's first-choice midfield target.
Arsenal are believed to be locked in negotiations with Sampdoria, and Gianluca Di Marzio provided a fresh update today.
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According to Gianluca Di Marzio, Emery has been left impressed with Torreira's performances in Serie A, with the 22-year-old spending the last four years in Italian football.
Sampdoria sporting director Carlo Osti told Italian broadcaster Rai Sport earlier this week: "Torreira has a €25m (£22m) release clause, everyone knows that".
According to Football Italia, Gli Azzurri had agreed to pay the €25 million release clause for the Uruguayan worldwide and were in advanced stages of contract negotiations, when Arsenal made a competing bid. Until now, Torreira has made just three substitute appearances for the national team but Unai Emery's are wary that the midfielder's valuation may rise next month with a strong World Cup showing.