Williams deputy team principal Claire Williams denied in Baku that the British outfit had engaged in takeover talks with Russian billionaire Dmitry Mazepin.
Last week, a report from Italy contended that Mazepin - a major shareholder of Russian chemical giant Uralkali - was seeking to acquire a controlling interest in Williams.
The potential move was seen as a way for Mazepin to fast track the career of his son, 20-year-old Formula 2 racer Nikita Mazepin.
However, Uralkali eventually denied the story, and Claire Williams has now done the same.
"Yeah, I saw those stories, I paid little attention to them," said Williams in Friday's team principal press conference in Baku.
"I haven’t met Mr Mazepin to talk about that. We had a brief conversation in the mid-part of last year, but subsequent to that there have been no conversations.
"I’d just like to be really categorical about it: Williams is not for sale. I have no intention of putting Williams up for sale. I don’t see why we would."
Williams believes the team's current depressed state of affairs makes it vulnerable to rumors. But a sale of the team would defy business logic said the 42-year-old daughter of Sir Frank Williams.
"I think certainly in times like this, that the team is going through at the moment, these rumours always come up, but with a business head on, when you’re team isn’t doing well selling at this juncture wouldn’t be the right time to do so.
"I think you would only investigate that opportunity if you are doing well. That’s the right time to sell. But Williams is in this sport and has been for more than four decades and we’ve never wanted to sell.
"This is what we do; we don’t have anything else to do. So, it is not on the market. I don’t want to sell it to everybody.
©Williams
"I want to go out and prove that we can do what we are in this sport to do – and that’s to get back on the podium and to win races again.
"That may take us a long time, but it took Frank more than 10 years to do it when he first started in this sport, and I’m sure we’ll have a lot more stuff thrown our way, like we’ve had today, like we’ve had this year, like we had last year.
"But you don’t give up when times get tough. For me it’s a test of your character that you continue and to prove to everybody that you can do it.
"That’s certainly the belief everybody has at Williams: that we can do this and we’re not going to just give up because the moments have got a bit hard for us."
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