The Liga outfit have set their sights on the Uruguay international, who has been told he is free to leave the Gunners following two years at the club.
Italian side Torino are also long-term admirers of the 24-year-old, but Madrid are at the front of the queue for the midfielder - who they view as a replacement for Hector Herrara - and remain deep in discussions with the Gunners over a deal.
Torreira has already agreed to join Diego Simeone’s side, who completed the signing of his compatriot Luis Suarez from Barcelona on Wednesday night.
But talks with Arsenal have so far failed to reach a successful conclusion, with cash-strapped Atletico insisting any deal has to only be a loan for the season.
Arsenal, however, want to sell Torreira permanently to bring in money to help them land Partey, their priority target for the summer, before the transfer window closes on October 5.
Partey is currently at Atletico, but sources have confirmed to Goal that the Spanish side are so far refusing to even discuss the possibility of including the Ghana international in any deal for Torreira.
Talks between the two clubs are continuing, with Arsenal hoping they can reach some sort of compromise. Atletico, for their part, remain insistent that the only way Partey will leave this summer is if his £46 million (€50m/$58m) release clause is triggered.
Torreira, meanwhile, continues to train with Mikel Arteta’s squad and sources at the north London club have praised the professional attitude he has been showing throughout the past fortnight despite the uncertainty that currently clouds his future.
Arsenal would be open to the possibility of him joining Atleti on loan for the season, but only if the deal includes an obligation to buy next summer.
Those guaranteed funds would then at least help with a potential move for Partey before the October 5 deadline, with the 27-year-old understood to be very keen on a switch to Emirates Stadium.
But despite the appeal of a move to Arsenal, sources close to the player have told Goal that he is remaining 'calm' over the situation and will continue to train in the 'most professional manner' out of respect to Atletico.
The midfielder is happy in Madrid and will not try and force his way out of the club to try and engineer a move to England.
Partey and his representatives understand Atletico’s stance and he will continue to work as normal ahead of the new La Liga season while waiting to see if Arsenal trigger his release clause.
Should that happen, then Goal has been told it is very likely the player will quickly agree to a move to England.