According to US reports, the two sides have been talking about swapping Malone's News Corp stake, worth around $11bn (£5.8bn), for News Corp's 38% stake in DirecTV, worth around $9bn.
Malone, the power behind holding group Liberty Media, unsettled Murdoch by doubling his stake in News Corp in late 2004, since when the pair have been in on-off discussions over a swap deal.
Malone's stakebuilding forced Murdoch to set up a "poison pill" defence to ward off any attempt by Malone to seize control of News Corp.
The strategy blocks investors from taking their voting shareholding beyond 15% and existing shareholders with stakes above 15% are prevented from adding to their holdings.
However, this provoked a hostile response from other investors in News Corp, who brought a lawsuit that forced Murdoch to let shareholders vote on whether the "poison pill" defence should be maintained or cancelled at its annual meeting on October 20.
The approaching vote may have swayed Murdoch into trying to do a deal, which would see Malone give up his stake in News Corp.
However, the reports say that any deal would be complicated because Malone wants to keep his tax liabilities down. For the transaction to be tax free, News Corp would have to offer Malone an operating business it has owned for five years, according to a Merrill Lynch report.
News Corp took control of DirecTV three years ago.
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