The magazine said that according to Ecclestone, Liberty Media will transfer the first of two tranches of payment in the $8.5 billion (£6.3 billion) deal on Tuesday.
Recent media reports had said that British broadcaster Sky as well as a consortium of Liberty Media's sister company Liberty Global and Discovery Communications were also circling Formula One.
Fiat Chrysler's Chief Executive Sergio Marchionne earlier said the industry as a whole had a vested interest in stability for Formula One.
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"I’ve had this conversation with CVC in the past, I’ve had it with Bernie ... I think it’s important that we provide stability and a long-term view. I’m sure that will happen soon," he said.
Auto motor und sport said Ecclestone left it unclear what role he would play once a deal had gone through. It quoted him as saying: "I will do what I have always done. What role I play is my decision."
Formula One's biggest shareholders are private equity firm CVC Capital Partners [CVC.UL] with a 35.5 percent stake and U.S. fund manager Waddell & Reed with 20.9 percent. Ecclestone holds 5.3 percent of Formula One and his Bambino Trust has another 8.5 percent.
CVC and Liberty Media declined to comment on the auto motor und sport report. Waddell & Reed was not immediately available for comment.
(Reporting by Maria Sheahan; Additional reporting by Alan Baldwin; Editing by Andrew Bolton)
