The deal with CVC Partners, which owns F1’s parent company, may be announced in the next few weeks.
A spokesman for Liberty Media declined to comment.
According to the Times report, Liberty would initially take a 10-15% stake in the auto racing franchise for nearly $2 billion with an agreement to take over the sports business at some point down the road.
Chase Carey, a longtime exec under Rupert Murdoch who helped launch Fox Sports and Fox News, is expected to be named chairman of F1.
A potential Liberty Media alliance would value the Formula One business between $8 billion and $9 billion, which has quickly grown since 2005 when CVC, a private equity group, took a controlling stake in the popular sports business. At the time, F1 was valued under $2 billion.
Other suitors reportedly in the mix for F1 included WME-IMG, private equity group Silver Lake and European broadcaster Sky.