Mr Murdoch divorced his second wife, Anna, earlier this month after 31 years of marriage. "My only comment on it is no comment," said a spokesman for Mr Murdoch.
Mr Murdoch, chairman of News Corporation, which owns The Times, Sunday Times, The Sun and News of the World, and British Sky Broadcasting, has three children from his marriage to Anna.
His daughter, Elisabeth, is head of programming at BSkyB. His son, Lachlan, who was made a senior executive vice-president of News Corp earlier this year as well as chairman and chief executive of News Ltd, the company's Australian arm, is seen as his heir apparent.
Ms Deng, an American citizen, who was educated at Yale, is also a divorcee. Mr Murdoch moved from Los Angeles to New York to be with her last year, moving into the Mercer hotel. The Australian women's weekly, New Idea, one of Mr Murdoch's publications, quoted sources close to him as saying that his children were "embarrassed" by the rapidity of his engagement, but Mr Murdoch's spokesman denied that this was true. "Mr Murdoch has no marriage plans," said the spokesman at the time.
Anna Murdoch filed for divorce last year citing "irreconcilable differences". News of the separation appeared in the Liz Smith gossip column of the New York Post, a publication that is also owned by News Corporation.