The prodigious product of a Los Angeles ghetto will attempt to back that claim on her Wimbledon debut this week, fearless of facing Hingis, Sanchez or Seles. But in the unlikely event that she is the ultimate winner in two weeks, Williams senses that her triumph will be devalued by the absence of her most significant rival - and we are not talking Steffi Graf here. Williams believes, moreover insists, that her main challenges will not come from the established order, but from a player yet to play a professional tournament - her younger sister Serena.
At 15, Serena is a year's experience behind her much vaunted sister but is definitely on a par when it comes to talking a good game. And if the experts who got it right with Venus are to be believed, then Serena has every right to bang her own drum. "Am I here to play in the Wimbledon juniors?" Serena said with incredulity, "I'm too good for that, I'm far too good for the juniors. I'm just here to be with Venus and gain some experience for when I play Wimbledon next year, which I definitely will."
A giant of a girl, with identikit beaded hair to her sister, Serena is young enough to play in junior events for the next three years, Venus, who was 17 on Tuesday, for another two, but thinks it amazing that anyone should consider her anything other than a leading professional - even though few people have heard of her, let alone seen her play. Mind you, that has not prevented Reebok from ploughing millions into her development, as with Venus.
And she calmly explains why it is so "stoopid" to ask her about being a junior, fear of failure and how the Williams clan - father Richard and mother Oracene are never far from sight - plan to dominate both the business and sporting worlds of tennis.
"I plan to play a couple of tournaments next month, at San Diego and Los Angeles, and then possibly four events after the US Open," she said. "So far, I've played a couple of junior tournaments in California but I'm so far beyond that level.
"Of course there are some good juniors out there, who also want to make the grade. But I already consider myself a professional - that's where I want to compete and not as a junior.
"I know what I'm doing because I've been working towards this since I was four. I've always known what I want to do and have never doubted that I will succeed."
The Williams way has attracted sponsors and attention in large quantities, but not many friends in the locker-rooms, where their ruthless ambition is seen as a lack of respect for the game and its players.
They now all live in a Florida mansion, with two courts in the back garden, and the girls are shortly to open a giant shop, peddling their own range of clothing. But it is only a few years since they were dodging bullets on a public court in the gangland area of Compton with barely a penny to their name.
At the insistence of Oracene, Richard was dispatched to confront and placate the warring gang leaders, whose drug wars on neighbouring streets were making the Williams training sessions a little too exciting. Fortunately, for all concerned, he was so successful that the gangs actually began to guard the court, guns at the ready, from potentially disruptive passers- by.
Now, the memories of diving for cover from gunshots makes the girls laugh, but they have also given them a sharp, independent streak. They often walk around holding each other's hand, but there seems to be no room for outside friends.
"Venus and I are very much loners when it comes down to tennis," Serena said. "We tend to just hang out together. I say 'hi' and stuff to the other players but I'm not best friends with them. They are opponents and you have to remember that you have to beat them.
"Even Venus and I only practise together when we are on the road but hit with different people at home. I guess that will change because soon we are going to be on the road forever. It is my dream that we will both be at the top together - that is why we have worked so hard."
Unlike Hingis and other teen queens, the Williams sisters are only gradually being introduced to tournament play by their father-coach Richard, who is fearful of a Jennifer Capriati style burn- out. Both still study and are devout Jehovah's Witnesses, though they share John McEnroe as their idol.
"My dad says that it is bad to play too much too young so we are just taking things gradually. Plus it's difficult for me because I am too young to play regularly under the current rules. There is a time for everything and we have other things to do too," Serena said. Such as? "We are also setting up a business together - we're entrepreneurs as well as tennis players. We're going to sell all sports things from our own tennis stuff to surfing and skateboarding equipment. Venus and I surf a lot and we also play the guitar together. The others like Martina and Anna can have their turn, they've worked hard for it too, but I'll have mine. It is my life goal and I don't think about failure. If I should get injured then there will be the sports business to fall back on." Fifteen-year- olds can be very convincing and it is just a shame that it will be 12 months before we can decide for ourselves. So perhaps we should make the most of Venus this year, because next she might be eclipsed.