The 30-year-old midfielder who crashed out of the World Cup recently is aware of Arsenal's interest in him but insisted that his family is settled in Spain and wants to continue playing in the La Liga.
Sampdoria's Uruguayan midfielder Torreira is understood to be the next player through the door at the club, with a £26m deal with the Italian side reportedly now wrapped up following Uruguay's elimination from the World Cup.
Today, Lucas Torreira is flying-in to London to undergo his medical with Arsenal...
And his current team, Sampdoria, agreed a £25million fee with Arsenal for a transfer during the competition in Russian Federation.
Torreira would be Arsenal's fourth signing of the summer after right-back Stephan Lichtsteiner, centre-back Sokratis Papastathopoulos and goalkeeper Bernd Leno.
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And over one million people have watched a video on Twitter that highlights the passion in which the Reds' midfielder goes about his business in the Three Lions' own box.
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Possibly a lame excuse in England's defence - for the '74 and '78 World Cup finals - only 16 teams were in both showpieces. In the end, we want to entertain where we possibly can.
La Celeste lost 2-0 to France on Friday, and the team will be heading home, but he will not be joining them straight away.
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.
According to a report by Spanish publication AS, Sevilla are holding out for a whopping £31 million for reported Arsenal and Tottenham Hotspur midfield target Steven N'Zonzi this summer. According to Le 10 Sport in France, West Ham and Everton are also keen on the French midfielder, who is preparing for a World Cup semi-final against Belgium this week.
Football London claim Torreira is now due to fly to London from Russian Federation to undergo his medical with Arsenal as Emery wants the transfer wrapped-up as quickly as possible with pre-season preparations already well underway.