The 51-year-old was sacked in February 1995 after Arsenal were given a preview of a Premier League report into alleged payments made to Graham by an agent following two transfer deals.
That punishment was compounded four months later when the FA imposed a world-wide year-long ban on Graham when the so-called "bung-busters" announced that he was guilty of illegally cashing in on the deals which took the Danish international John Jensen and Norwegian Pal Lydersen to Arsenal.
"I can't wait to get back into a job - but it seems I will have to be patient," Graham said. "Sadly, the only reason you get a job in this game is when somebody else loses it. Only two clubs parted with their managers last season and the year before that it was, I believe, about 13.
"But whatever happens now, I am not going to settle for joining just any club. It has got to be one that has big ambitions, whether in England or abroad."
Graham, who won six major trophies - two League Championships, two League Cups, one FA Cup and a European Cup Winners' Cup - in eight years at Highbury, added: "The success I had with Arsenal proves, I believe, that I am a winner. And I want to take on a club that has the same attitude."
It was widely expected he would march into Leeds and take over the team from his close friend Howard Wilkinson - with another pal and neighbour, Richard Thompson, the former Queen's Park Rangers chairman, trying to buy a controlling interest in the Yorkshire club.
Thompson's Elland Road bid, through his Caspian group, is expected to get the green light today.
But Graham said: "All you are hearing is speculation and there is no chance I would try to go behind people's backs to get a job. Howard certainly deserves much better than that."
Graham is also aware that Terry Venables is also back in the marketplace. "Terry and I have been pals from way back - and rivals too," Graham said. "It looks as if that could continue now with us both going for the same sort of jobs. I don't mind where I go so long as the challenge is appealing. I need it after recharging the batteries for so long."