Talks with CVC Partners, which owns a 35 per cent stake in F1, are at an advanced stage, reports The BBC.
Liberty Media has stakes in several sports and entertainment businesses, including the Atlanta Braves Major League baseball club.
A source close to the deal told BBC Sport that an agreement is yet to be completed, and other interested parties remain in talks.
Others that have considered buying into F1 include, Qatar Sports Investments, and Stephen Ross, owner of the Miami Dolphins American football team.
CVC has held a stake for the past decade but sold some of its holding in 2012.
A sale would end years of speculation and rumours about a potential change of ownership for the motor sport.
German magazine Auto Motor und Sport said the deal had been confirmed by F1 chief executive Bernie Ecclestone and was worth $8.5bn (£6.5bn).
