The Gunners are open to offloading the Uruguay international this summer and he has attracted interest from Torino and Fiorentina.
But Atletico are currently leading the race and remain in talks with Arsenal over a possible deal.
According to AS, Atletico want to sign Torreira on loan with a non-mandatory option to buy at the end of the season.
However, Arsenal’s preference is to permanently sell Torreira and are demanding a €24 million (£21.8m) transfer fee.
The report also claims that Suarez, who is on the verge of joining Atletico after an agreement was reached with Barcelona on Wednesday evening, has endorsed Torreira’s move to Diego Simeone’s side.
Suarez had initially played a key role in Torreira’s move to Arsenal in 2018 as he recommended the signing to Raul Sanllehi, who was the Gunners’ head of football at the time of the transfer.
‘Luis Suarez was very helpful,’ Torreira said shortly after making his Arsenal debut.
‘He spoke to Raul, who brought many players to Barcelona. I was really grateful to Luis and only a short time ago I sent him a message of thanks.’
And now Suarez, who plays alongside Torreira with Uruguay’s national team, is keen for the midfielder to join him at Atletico.
The 24-year-old has not yet made an appearance for Arsenal this season.
‘I am not making decisions because players might leave or stay, it is just for the players we see every day who are in the best possible condition to compete and get us closer to winning football matches,’ Arteta said when asked why Torreira did not even make the bench against Leicester.
Asked if Torreira could be leaving Arsenal before the end of the window, Arteta said: ‘Again, I cannot discuss any internal things.’