The Uruguayan is not part of Mikel Arteta's future plans at Arsenal and is wanted by Atletico coach Diego Simeone, a long-standing admirer of the former Sampdoria player.
Standard Sport understands Atletico's new signing, Luis Suarez, has also given his blessing to the arrival of his compatriot – having also recommended Torreira to Arsenal's former Head of Football Raul Sanhelli in 2018.
Torreira, who is also being tracked by Torino, is keen to join Atletico.
However, the deal has been complicated because Atletico are keen to seal a loan move without an obligation to buy the midfielder, while Arsenal want to make a permanent deal compulsory.
In addition, Atletico need to remove more players from their wage bill and hope to sell or loan Mexico midfielder Hector Herrera in the coming days, which could further delay the completion of this transfer.
Atletico still hope to keep midfielder Thomas Partey, a long-time target for the Gunners, and the Ghanaian is not part of the negotiations for Torreira.