It is just a rumor… but it is not the first time this rumor has surfaced. Forbes magazine was among the first to think that this could happen. At that time (2011), the rumor was strictly based around business advantages:
It appears as though Liberty Media is preparing to unload the Braves. The tax advantages to Liberty’s purchase of the Braves from Time Warner 2007 expire after five years and ownership has slashed player payroll from $102 million to $84 million since 2008 despite higher revenue.
At that time, the company responded by quashing the rumor, both in public comments and in reality as no sale occurred, of course.