Torreira joined the club from Sampdoria 12 months ago and has performed well.
However, the diminutive midfielder has been linked with a departure amid reports he’s unhappy in London.
Serie A giants AC Milan have been touted as potential suitors.
When quizzed last week about life in England, Torreira wasn’t too enthusiastic.
“You want people who really want play for the club”
“London is a completely different world. England is a very big country,” he said.
“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.”
Parlour has warned that Arsenal could be forced into selling their influential star.
The Gunners have only limited transfer funds this summer.
Torreira, who is contracted until 2023, would likely command in excess of £30m.
“The players have got all the power these days, I must admit,” Parlour told Starsport.
“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.”
* Ray Parlour was speaking at the McDonald’s & FA Fun Football Festival at Ryan FC. These festivals are taking place across the UK this summer, giving thousands of children the chance to enjoy the game. Find your nearest festival at www.mcdonalds.co.uk/funfootball