Rumours spreading across the City suggest that Sky is lining up deputy chair Nicholas Ferguson to replace Murdoch. Speculation has heightened after Ferguson announced his decision to step down as chairman of private equity firm SVG.
Murdoch today expressed his "deep regret" over the phone hacking scandal that has engulfed News International, the newspaper publisher where he acted as executive chairman until recently resigning the post.
The youngest son of media mogul Rupert Murdoch has also recently resigned from the board of drugs giant GlaxoSmithKline, as well as the boards of publishers of various newspapers, including The Times and The Sun.
Murdoch is thought to be keen to now focus on developing the non-US pay-TV businesses within his father's News Corporation empire, and has been praised for his leadership of Sky, including a successful previous stint as the firm's chief executive.
However, he has faced widespread criticism of his handling of the phone hacking affair at News International, leading to 45% of independent shareholders in Sky opposing, or abstaining in a vote over his re-election as Sky chairman last November.
Sky did not comment on the latest speculation. But the Evening Standard says that Sky insiders have played down the chances of Ferguson replacing Murdoch as chairman, and noted that his exit from SVG was part of a pre-planned reshuffle.
However, another dimension to this could be Ofcom's review of whether James Murdoch and News Corp are 'fit and proper' to continue to be involved in Sky.
Should sufficient cause for concern be found in its review, the regulator warned that it could revoke Sky's UK broadcast licence unless Murdoch quits the company's board, or News Corp sells its 39.1% stake in the business.
It is not expected that Ofcom would actually go through with this threat against Sky, the UK's second-biggest TV platform after Freeview, but instead the regulator could be looking to encourage Murdoch to exit the broadcaster voluntarily, or dissuade News Corp from attempting another takeover of the firm in future, following the abandonment of a controversial bid last year.
Meanwhile, James Murdoch has reportedly written to MPs on the Culture Select Committee expressing his "deep regret" over the hacking scandal, but again stressed his innocence in the matter.
The letter, reported by the Financial Times but due to be published by the committee today, comes a day after former News International chief executive Rebekah Brooks was arrested and bailed on suspicion of conspiracy to pervert the course of justice.
Murdoch's letter is said to accept responsibility for not uncovering phone hacking earlier, and also offers another apology for the widespread invasion of people's privacy by the now defunct News of the World.
However, the executive reiterates his long-held position that he did not mislead the MPs when he claimed that he was not aware of the scale of the hacking when he agreed a major payout to Gordon Taylor, the chief of the Professional Footballers Association, in 2008.
He also said that his decision to quit News International was an opportunity to concentrate on News Corp's global pay-TV business, and had nothing to do with distancing himself from the ongoing scandal at the publisher.