According to TeamTalk, the transfer deal with Sampdoria was agreed some time last month, but the player confirmed that he turned down the chance to undergo his medical in Russian Federation - claiming he did not want to be distracted from his World Cup duties.
Arsenal asked Torreira to fly straight from Russian Federation to England and, having touched down in London, he is expected to undergo a medical at London Colney on Monday.
Emery has already brought in three signings, with Stephan Lichtsteiner joining from Juventus on a free transfer, while goalkeeper Bernd Leno and Sokratis Papastathopoulos have also been acquired form Bayer Leverkusen and Borussia Dortmund respectively. Is Torreira more a cross between N'Golo Kante and ex-Gunner Santi Cazorla?
And according to French outlet Ouest-France, Lorient midfielder Guendouzi will under go his Arsenal medical today.
The midfielder flew-out to Russian Federation with the Uruguay squad without resolving his future but Football London claim Arsenal agreed a £26.5m deal with Sampdoria and have already settled on terms over a four-year contract.
Torreira was a key part of the South-American team who were knocked out by France on Friday.More news: Frustrated Cousins called Warriors to get deal done
A number of those back in training are expected to feature when the Gunners kick off their pre-season fixture list with a trip to non-league Boreham Wood on Saturday.
The 24-year-old made his name at Benfica and then Valencia before making his big move to the Nou Camp but it now appears as if his time at the Catalan giants could be coming to an end.
The paper explains that Sociedad are on the hunt for a replacement for Alvaro Odriozola, who left the club for La Liga giants Real Madrid last week, and believe that they may be able to lure Monreal back to Spain.
Torreira was one of Uruguay's top performers in a defensive midfield role, as he helped his country reach the quarter-final stages.
Emery's first game in charge of Arsenal will be the pre-season game against Atletico Madrid on July 26.