The 35-year-old joined the Gunners in the January transfer window and has made an impact at the Emirates.
“I fancy staying, of course I do,” Campbell told the club’s official website.
“I want to stay and I want to give it my all for at least another year. I could do two, but the manager never gives out two. We always want a little bit more.
“Give me one year and I will work every day and try to win a trophy and bring some kind of glory back to Arsenal.”
Campbell continued: “Deep inside I feel I have got two real gritty years left in me, the years in which I can affect things.
“If I am in the team I can really make a difference. I know that. And after two years I will look at it again and we’ll see.
“After that I might only be able to play games here and there, who knows, but I think I can be an influence and be positive and win games and be strong for two years.”
He added: “We will sit down, it has started and we will try to thrash something out.
“The negotiations are either going to be done in a week or two or it might take until July – you just don’t know how things will pan out.
“We will have to see how Arsene sees me at the club.”