The midfielder, 28, is under contract with Arsenal until 2018 but speculation over his future has been widespread.
"It is definitely my preference to stay," the German said on Wednesday.
"Once everyone is back in London, we will sit down and discuss the future. I have always said that I feel very good at Arsenal."
Arsenal face Sydney FC on Thursday (11:00 BST) and Western Sydney Wanderers (11:00 BST) on Saturday before heading to China for two further games.
Arsene Wenger's side meet Bayern Munich (12:20 BST) on 19 July in Shanghai and Chelsea (12:40 BST) on 22 July in Beijing before returning to England.
"For now the most important thing is our pre-season and getting through the tour, training and getting fitness," added Ozil, who joined Arsenal from Real Madrid for £42.4m in 2013.
"I have always said that I feel very good at Arsenal."
'I don't know about my future'
While Ozil appears keen to stay, the futures of Chile forward Alexis Sanchez and France striker Olivier Giroud remain less clear.
Giroud, 30, has been with Arsenal for five years but has been linked with moves to Premier League rivals Everton and West Ham.
"I've been through some difficulty this last year, but always succeed to bounce back," said the former Montpellier forward.
"I'm still an Arsenal player and try to be professional like I always have done and to prepare well for the next season."
Meanwhile, Sanchez has been linked with Manchester City.
"It would hit the team quite hard if he left because he is a player who always delivers," said Ozil.