The 33-year-old Czech midfielder is out of contract in the summer, but Arsene Wenger and the player have already confirmed their willingness to agree fresh terms.
Because of his age, Arsenal's policy is to hand the player a one-year deal and that should soon be concluded.
"Arsene Wenger wants me to stay, he wants our co-operation to continue. I want to stay," he told Czech News Agency CTK.
"Hopefully all is sorted out in the next few days. It would be great to play on at Arsenal for another few years."
Meanwhile, Rosicky insists that despite the weekend defeat to Stoke, they could still win the title.
"It was a huge loss of points. On the other hand, there are still ten games left," he insisted.
"In the season in which we won the title with Dortmund, we lost to Kaiserslautern a few rounds before the end and in the dressing room we were talking 'Well, this is over now.'. Suddenly, we won all the remaining games and had the title in our hands."
Rosicky also talked about his future with the Czech Republic national side, and has met with new coach Pavel Vrba about playing on.
"It was not easy to make the decision (to carry on), I can tell you that," he said.
"When we were speaking to each other then, there was a lot of question marks surrounding me.
"I didn't know if I would be staying at Arsenal and I didn't know if my age wouldn't be an obstacle to Mr Vrba. At the end of the qualification (EURO 2016) I will be 36 and you never know what your health will be like.
"But why should I end with something, when there is no need to? My health is good and football-wise, I think I still have goods to offer.
"These factors played in favour of me carrying on. We are now all full of expectations and hopes for the Euro 2016 qualification and want to reach the finals, understandably."
"I don't feel like I'm turning for the worse or that my level of performances would be dropping. There has been no decline yet.
"You can look at Ryan Giggs and Pavel Horvath, who both play at an advanced age. I would like to play this long too, but we will have to wait and see what future brings."