John Malone’s Liberty Media Corp. is making a play for iHeartMedia Inc., offering to pump $1.16 billion in cash into the nation’s largest radio broadcaster in return for 40% stake in the reorganized company following an eventual bankruptcy filing.

A deal between iHeart and Liberty, which owns Sirisu XM, presents the possibility that Mr. Malone could combine the biggest radio broadcaster, scrubbed of billions in debt after bankruptcy, with the leading player in satellite radio.

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