Liberty -- which owns 53 percent of Sirius XM -- offered a stock deal Friday valued at $10 billion that would give SiriusXM shareholders a 4.5 percent premium over Friday's closing stock price, the Los Angeles Times reported Saturday.
Sirius said it would form a special committee to consider the offer, and the committee and its shareholders needed to approve the deal before the board would agree to it.
The deal puts a value of $3.68 per share on SiriusXM stock, and SiriusXM shareholders would end up with 39 percent of the outstanding common stock in the parent company.
"Our proposal will allow Sirius public shareholders to convert from a non-controlling stake in a subsidiary into a direct equity position in Liberty, the parent company," said Greg Maffei, Liberty's chief executive officer.
Liberty, which owns the Atlanta Braves baseball team and 27 percent of cable company Charter Communications, is controlled by billionaire John Malone.
"We believe the combined company will have better access to capital and all of Liberty's shareholders -- both its current shareholders and the Sirius shareholders who become Liberty shareholders as a result of the proposed transaction -- will enjoy enhanced liquidity as shareholders of a $27 billion market capitalization company," Maffei said.