Murdoch's taxes came under scrutiny in Australia and now he wants Google to get same treatment.
Twitter's share price jumped more than 12% on the rumour before easing to close 4% higher in New York.
Entertainment editor Toyin Owoseje rounds up the celebrity stories of the week.
Engagement notice posted by 84-year-old media mogul and Texan model in The Times.
The announcement was made in Murdoch's Times newspaper.
Prime minister attends select pre-Christmas drinks party at Murdoch's home in St James's.
The government is facing calls to release details of MPs' meetings with media groups.
Prosecutors say there is 'insufficient evidence' to bring any cases against individuals or companies.
Investigations into Rupert Murdoch's newspapers and the Mirror Group have now been dropped.
Chairman Peter Harf said they were very pleased to welcome the media mogul on to the board.
Murdoch, 84, and Hall, 59, are said to have been introduced by his sister and niece in Australia
Sky reported a 10% rise in quarterly operating profit for the three months to the end of September to £375m.
Watson under fire over Leon Brittan comments and claims of Westminster paedophile ring.
Labour would rather have the chance to move the goalposts back in a leftward direction.
Activist MP Tom Watson has been elected Deputy Leader of the Labour Party.
National Geographic bought by 21st Century Fox for $725m
Brooks is back with Murdoch at News UK and September is a time of rebirth for other bosses too.
Mark Hanna threatens to blow the whistle on 'one of most hated organisations in the UK' in protest at Brooks' return.
Tony Gallagher hit the headlines in 2014 when he took a job in the kitchen of a trendy London restaurant.
Brooks to head Murdoch's UK news operations just over a year after being cleared of phone hacking.
Brooks was earlier acquitted of all charges related to the phone-hacking sandal at the News of the World.
The media mogul said Corbyn was the 'only candidate who believes anything, right or wrong'.