Under Olympic Games rules, Cooper would have to have Australian citizenship to be eligible to compete for the Wallabies sevens team.
It was recently discovered that Cooper had been travelling on a New Zealand passport despite leaving the country of his birth in 2001 at the age of 13.
Cooper said he would now turn his attention wholly on his club's bid to win the Top 14 title.
"The club has been very accommodating with the sevens and now knowing that sevens isn't in the future, without being able to secure the passport and citizenship, I owe the club to play well and enjoy my time here, just focus on RCT and playing the finals and the future of the club," the 28-year-old said.
Cooper has had a tough time adjusting to Toulon, outspoken club president Mourad Boudjellal notably comparing his performances to Jonny Wilkinson as going from "foie gras to pate".
But when asked whether he would like to stay on with Toulon, the Wallaby said: "I hope so. I came here right at the end of the season. It was very difficult to settle in as quick as I wanted to after the World Cup, with the sevens.
"I'm grateful to the club for being accommodating to allow me to pursue those goals. Now they're finished and I have to put my focus into repaying the club for the faith they've had in me so far.
"Going into the future, I don't have a crystal ball that I can predict what's going to happen in the future, but I would love to continue on and also play some good football and enjoy it."
- news.com.au