US conglomerate Liberty Media said Friday it wants to buy the shares it does not already own in satellite broadcaster Sirius XM in a stock swap deal worth some $10 billion. The holding company controlled by tycoon John Malone announced the proposal which would give Sirius public shareholders a 39 percent stake in Liberty Media. "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 president and chief executive. "Sirius shareholders will continue to participate in Sirius' future prospects along with Liberty's broader portfolio of businesses and opportunities. 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." The offer at $3.68 per share represents a 4.5 percent premium for Sirius shareholders. Liberty, which owns stakes in a variety of companies including cable operator Charter Communications and the entertainment operator Live Nation, bought a stake in Sirius in 2009 for $530 million. Its current stake is some 53 percent. Liberty also owns the Atlanta Braves baseball club.