According to a report in the Sunday Telegraph, all the candidates in the race will have to undergo the tests in the battle to succeed Tony Ball as chief executive of BSkyB.
"All the candidates will sit a psychometric test, including James," an unnamed executive source close to BSkyB told the Sunday Telegraph newspaper.
The tests are based on theories developed by Swiss psychologist Carl Jung and involve an evaluation of a person's personality, intelligence and aptitude.
Investors are concerned that the 30-year old son of Rupert Murdoch will be given the job without a real search being conducted. They are worried that Murdoch Snr would use the appointment of his son to consolidate his control over Sky, in which News Corporation holds a 35.4% stake.
Headhunters Spencer Stuart have been appointed and they will conduct the initial round of interviews.
So far, a number of names have emerged alongside James Murdoch. These include two internal candidates in BSkyB chief financial officer Martin Stewart and chief operating officer Richard Freudenstein.
Stewart is being seen as the City's favourite candidate to replace Ball. The other potential candidates mentioned are Jim Robbins, chief executive of US cable giant Cox Communications, and Michael Dugan, the president of EchoStar, rival satellite broadcaster to News Corp's DirecTV.
However, many are already betting that James Murdoch, who currently runs the Asian pay television group Star TV, is something of a sure thing for the job.
At the weekend, speculation that James is set to be installed intensified after Peter Chernin, president of News Corp and Murdoch Snr's right-hand man, threw his weight behind the 30-year old and said he was "best man for the job".
Speaking at a conference in France, Chernin said: "James is a remarkably talented executive. I don't think there is anybody in the pay-television industry that has had the success he's had over the last three years. We believe James is the best person to do this job. He either has or will be applying."
Chernin added that News Corp had never done anything at BSkyB that was not in the best interest of that company.
"I think the results speak for themselves. I don't think anyone can point to a single instance when News Corp has benefited at the expense of BSkyB shareholders. It's not like we've been raping the company," he said.
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