The French centre-back, who has been a key figure in the Gunners' defence for the last three years, remains focused on winning silverware in North London.
Saliba, whose performances have caught the attention of top European clubs, was asked about his future ahead of Arsenal's Champions League round of 16 second-leg clash against PSV on Wednesday.
While acknowledging interest from elsewhere, the 23-year-old made it clear that his priority is to stay at Arsenal and help the team succeed.
His contract at the Emirates runs until the summer of 2027, but Arsenal have yet to open talks over an extension.
Despite this, Saliba remains dedicated to the club's ambitions, with Mikel Arteta's side still competing on multiple fronts this season.
"Not yet, because there is some years (left), so there is no rush at the minute. I'm happy here, that's it. I want to win big things with Arsenal," said Saliba.
"If you leave this club without winning anything, the fans will forget about you. I want to win big things here.
"I want to be one day the best defender in the world. I know I have to work a lot and to win trophies as well - but that's my dream.
"I think I am not so far, but I am not the best at the moment because, for me, this season I have not been so good. I have to review my season, I have to work on my game. But this season, I have not been so good.
"I have to watch especially my partner, Gabriel, who has been so, so good this season. There are a few (defenders better than me), but of course, I have to focus on myself and work more."