The controlling stake in F1's parent company is currently owned by CVC Capital Partners, which has a 35 per cent stake and has held its position since 2006.
According to Sky News, which first reported the story, if the deal goes ahead as planned, F1 will also become a listed company on the Nasdaq exchange in New York.
Liberty Media's acquisition of a controlling stake is reported to be worth $8.5bn and will be taking place in two stages. The first stage, which could happen within a few weeks, would involve Liberty Media taking a minority stake, which would not be subject to regulatory conditions.
The second stage will involve Liberty Media taking a majority stake, which would be privy to regulatory conditions and may also require sign off from worldwide motorsport's governing body Federation Internationale de l'Automobile.
The potential deal could also involve 21st Century Fox board member and Sky director Chase Carey being appointed chairman, replacing Peter Brabeck-Letmathe, who is also the chairman of Nestle.
This would see Carey working alongside Bernie Ecclestone, F1's veteran chief executive, at least for a short period of time.
However, Liberty Media would not be without competition for command of F1. US private equity firm Silver Lake, which has a holding in Chinese retail giant Alibaba, entered talks with CVC for a stake back in May.
Meanwhile, ex-Sainsbury's boss Justin King last year denied he was vying to replace Ecclestone in F1's top spot.
CVC and Liberty Media both declined to comment. Goldman Sachs, Morgan Stanley and law firm Freshfields Bruckhaus Deringer, who are reported to be working on the deal, also declined to comment.
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