The Gunners emerged as contenders to sign the Uruguay international in the summer transfer window ahead of the World Cup.
Arsenal are looking to improve their options in the middle of the park following a disappointing 2017-18 Premier League season.
Torreira is reported to have a €25m contract release clause to make the Uruguayan an attractive proposition ahead of the major tournament in Russia.
However, Arsenal are willing to pay €5m over the release clause if Sampdoria are willing to accept the transfer fee in instalments rather than one lump sum.
Sky Sports News reporter Sheth provided an update on Arsenal’s pursuit of the South American ahead of Uruguay’s opening World Cup fixture against Egypt on Friday.
“We have been given info from our colleagues in Sky Italia this morning,” Sheth told the Transfer Talk podcast.
“We have been told there has been new contact between Sampdoria and Arsenal over Torreira.
“There is a clause in his contract of 25m euros but Arsenal don’t want to pay that all in one hit. They are willing to do it in a different way that would help Sampdoria and Arsenal.
“They will pay 30m in installments. We are told an agreement is close and they are discussing minor details.”
The 22-year-old midfielder scored four goals and made one assist in 36 Serie A games for Lazio last season.
Torreira has made just one appearance for the Uruguay national team after he made his debut in a 2-0 win over Czech Republic in March.
Arsenal signed Switzerland’s veteran captain Stephan Lichtsteiner in a free transfer from Serie A giants Juventus earlier this month.
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