Citing unnamed sources, the Journal said News Corporation has explored whether there are any potential buyers for News International, which includes British newspapers the Sun, the Times of London and the Sunday Times.
The unit also included the 168-year-old News of the World weekly, which published its last issue on Sunday after becoming embroiled in a phone-hacking scandal that shocked the public and drew a furious government reaction.
The Journal, which is also owned by News Corporation, said Murdoch himself has long opposed such a move and considers News International one of his favourite components of his media empire.
The Journal, citing the same sources, said that there did not appear to be any buyers because of the poor state of the newspaper industry, but said the company may revisit the idea in the next six months.
News Corporation's board has broached the idea of selling off News International on a number of occasions in recent years but that Murdoch himself always shot the idea down, the Journal said.
"It was basically one of those things where it was talked about for maybe two to five minutes and Rupert would say, 'No way,'" the Journal quoted a person familiar with the company as saying.
British lawmakers today were set to deal a body blow to Murdoch's bid for pay-TV giant BSkyB, as the phone-hacking scandal rocking his media empire threatened to spill over to the United States