The well-sourced German magazine Auto Motor und Sport said that the sport's veteran commercial ring-master Bernie Ecclestone had confirmed the deal at the Italian Grand Prix.
The magazine reported that Ecclestone said Liberty Media, backed by American media tycoon John Malone, will make the first of two payments on Tuesday in a deal valued at 8.5 billion dollars (7.6 billion euros, £6.5 billion).
If that goes through, according to well-informed paddock sources, current owners CVC Capital Parners, who hold a 35 percent stake, will leave the sport. CVC Capital Parners, who invested in the sport in 2006, previously sold a 21 percent share to US-based fund manager Waddell & Reed in 2012, while also selling shares to another American investment group, BlackRock, and Norwegian bank Norges.
Liberty Media Group, which is listed on the New York Stock Exchange, is expected to take control of the company that will run Formula One.
Ecclestone, 85, said his future with the business would remain in his hands. He told Auto Motor Und Sport: “I will do what I have always done. What role I play is my decision.”
Ecclestone, whose mother-in-law was kidnapped in Brazil recently, did not respond to questions about the sale when asked ahead of Sunday's race at Monza.
Others who have looked at a deal to buy the motorsport include Qatar Sports Investments, the owners of Paris Saint-Germain football club, and Stephen Ross, the owner of American football team the Miami Dolphins.
The sport's glamorous reputation has been hit in recent years by a lack of genuine sporting interest due to the domination of first Red Bull and then Mercedes, with global viewing figures dipping as a consequence.