NEW YORK — Liberty Media Corp. chair John Malone emerged from his corporate cloister Thursday to raise the possibility that News Corp. might swap its interest in the National Geographic Channel for Liberty’s sizable voting stake in Rupert Murdoch’s empire.

Malone’s remarks came during his annual sojourn to Gotham for Liberty’s investor conference, one of the few public events he attends.

Upbeat and relaxed, Malone extolled the strength of Liberty, which he said has been transformed from a holding company into an operating company largely on the strength of home shopping channel QVC. He also said he expects Time Warner to buy out Liberty’s 50% stake in Court TV in the near future.

Malone further suggested that Liberty might be interested in acquiring part of Barry Diller’s InterActiveCorp once Diller spins off the Internet travel part of the biz under the Expedia banner. Liberty’s 20% stake in IAC would give Liberty an advantage in any acquisition.

As Murdoch did last week, Malone stressed that Liberty and News Corp. are still in the negotiation phase and that some of the proposed solutions are quite complex since they would need third-party approval.

Such would be the case with Nat Geo, since any change in control would need to be approved by the National Geographic Society. News Corp. has a 66% stake in the docu channel.

Even before addressing an analyst’s question about unwinding the News Corp. stake, Malone said Nat Geo would fit in nicely with the Discovery Communications empire.

Insiders said while Nat Geo could indeed be in play, it is only one scenario being discussed by Murdoch and Malone.

Murdoch told investors last week that he’d like to resolve the matter in the next three months. Malone caught Murdoch by surprise when snapping up enough voting shares to give Liberty an 18% stake in News Corp., uncomfortably close to the 30% stake owned by the Murdoch family.

Murdoch also said he wasn’t interested in Liberty’s Starz Entertainment Group. Some Wall Streeters have speculated that Malone might suggest swapping Starz.

“We continue to look at a win-win situation for both of us. We have a couple of theories how to do this, but there is nothing publicly to discuss,” Malone said. “I can report that relations are good.”

Casting off

Malone informed investors that he expects the spinoff of Discovery Holding Co., which will include Discovery and post-production company Ascent Media, to occur in the next several weeks once Washington issues the requisite tax ruling.

Unlike an initial public offering, a straight spinoff can be tax free with approval from the IRS.

Like Viacom and Clear Channel, which are planning spinoffs, Liberty said the breakup will ultimately increase shareholder value by giving the smaller entities greater access to the capital markets and a more direct line to investors.

When asked about getting back in the cable system biz, Malone said he considered hooking up with Charter Communications and making a run for bankrupt cabler Adelphia, but it was too expensive a proposition. He said to be in cable these days requires scale, something Liberty doesn’t have.

Liberty shares closed down 1¢ at $10.48 on Thursday.