The Guardian say that the Gunners had officials in Milan yesterday to discuss personal terms with the midfielder's representatives having reached an agreement with Sampdoria.
Arsenal have seen two well known players leave the Emirates this summer, injury riddled midfielder Santi Cazorla, who served admirably with the team for six seasons and the retiring German worldwide Per Mertesacker.
While talks are ongoing between the clubs its understood that no agreement has been reached yet between the two sides, with Torreira now with his country ahead of the World Cup.
It is understood that there is ongoing contact between the clubs and that the deal will hinge on the structure of the payments, with Arsenal ready to spend in excess of £25 million if the fee is spread over several years.
Signing the German shot-stopper as well would see all of the Spanish manager's budget spent, albeit with money raised from any player sales likely to be made available for further strengthening.