Arsenal face a major fight to hold onto their Gabonese striker with Barcelona monitoring the player ahead of the transfer window reopening in January as they seek a replacement for Luis Suarez.
Pierre-Emerick Aubameyang, 30, has not yet made a decision to renew his contract with Arsenal since joining in January 2018.
The report claims that the midfielder is concerned that he could jeopardise his chances of playing in next year's European Championship, should Switzerland qualify, if he loses his place at the London club.
Torreira joined Arsenal in 2018 from Serie A outfit Sampdoria after an impressive showing for Uruguay at the World Cup that summer.
He hasn't played since and Gunners boss Unai Emery opted to remove the 27-year-old from the squad's leadership group, seeing the armband now go to Pierre-Emerick Aubameyang.
He has been ultra-prolific since completing his deal, scoring 10 Premier League goals in 13 appearances in his debut campaign, before winning the Golden Boot last season after netting 22 league goals. However, Arsenal have so far struggled to tie their new club captain Aubameyang down to a new contract.
This is because he was attracting a lot of abuse from the club's fans and in order to protect him from the abuses, he has been benched and may not wear the Arsenal colours again.
Many Arsenal players are reportedly wary of committing their futures to the club while there is so much uncertainty surrounding manager Unai Emery's future, with senior players harbouring a number of doubts about the Spaniard.
"It's a very big game, a game we have to win", he said.
Barcelona will look to tap into the chaos at Arsenal, to secure the 50 goal striker for a cheaper price.