A man acquired from Sampdoria in the summer of 2018 has hinted that another move could be on the cards.
Speculation regarding a player who largely impressed during his debut campaign is the last thing that Unai Emery needs in a window that the Gunners are said to have limited funds at their disposal.
Parlour believes the Spaniard needs to be getting a quick decision from Torreira on his future, with the current uncertainty doing nobody any favours.
The former Gunners winger told the Daily Star: “The players have got all the power these days, I must admit.
“I think that sometimes the family doesn’t settle, but we’ll have to see with that situation.
“He’s a good little player, but he felt the pace towards the end of the season and dropped off a little bit.
“He had a really good start to his Arsenal career and looked a really lively character, which we’ve been lacking.
“But again, as a manager and club, you’ll sit down and find out why he’s not enjoying it.
“Sometimes if they want to go and leave there’s not a lot you can do about it.
“You want them to stay, but if they’re not happy the performances on the pitch won’t be as good as they should be.
“It’s another dilemma for Arsenal. You want people who really want play for the club and do their best.”
Torreira claims to have found settling in England testing, with the 23-year-old South American experiencing quite the culture shock in north London.
He said: “London is a completely different world. England is a very big country.
“I had trouble with the language, communicating with my team-mates and with the people.
“It's pretty rough in certain moments when you can't have any dialogue, that's the most important part.
“The weather is also difficult. You go out in the morning and it's cloudy and you get back after training and it's still cloudy.”
Torreira is tied to a contract until 2023, but it remains to be seen whether Arsenal can talk him into staying put and seeing that agreement through.