The Colorado-based Liberty, which is controlled by billionaire
The all-stock transaction would be valued at about $10 billion.
Liberty currently controls about 53% of SiriusXM.
In a statement, SiriusXM said its board would form a special committee to consider Liberty's proposal. Eddy Hartenstein, the publisher of the Los Angeles Times, serves on the board of SiriusXM.
SiriusXM also said the deal "would be conditioned on the approval of both a special committee and a majority of the public stockholders of SiriusXM."
Under the proposal, SiriusXM common stock holders would receive new Liberty Series C shares. Liberty would provide a slight premium -- 4.5% -- over the Friday closing price of SiriusXM.
The proposed exchange ratio of 0.0760 would value SiriusXM common shares at about $3.68 per share, Liberty said. Current shareholders of SiriusXM would then hold about 39% of the outstanding Liberty common stock. The SiriusXM board members could try to demand a higher price.
In 2009, Liberty rode to the rescue of then-cash-strapped Sirius subscription radio service during the height of the financial crisis by providing loans of more than $500 million. In exchange for the loans, Liberty received preferred stock in the satellite radio company. In recent years, Liberty has further consolidated its control.
"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," Greg Maffei, Liberty's chief executive, said in a statement.
"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.
Last fall, Liberty announced a plan for SiriusXM to use its cash to buy back about $500 million of its shares held by Liberty, part of a $2-billion stock buyback program.
Liberty also owns the Atlanta Braves professional baseball team and a 27% stake in cable company