Rebekah Brooks is to be questioned by a committee of Members of Parliament (MPs) on phone hacking on Tuesday.
Rupert and James Murdoch have been served with a summons to attend, reports Telegraph UK.
Ms Brooks, the Chief Executive of News International, has agreed to give evidence to the Commons Culture, Media and Sport Committee.
Rupert Murdoch and his son James were both also invited to attend the committee but declined, saying they were not available on Tuesday.
MPs have now invoked the rarely used power of summons to attempt to compel them both to attend.
The summons has been delivered to News International headquarters at Wapping, but it was unclear today whether the bid would work.
There are conflicting interpretations of whether the power can be applied to the Murdochs as they are not UK citizens.
It is understood that if the Murdochs ignored the summons, the House of Commons could vote to that they are in contempt of Parliament, reports the Telegraph.
The procedure has so rarely been used that MPs are uncertain about what the implications of this step would be.
Committee chairman John Whittingdale said the committee were seeking advice.
The letters from the Murdochs declining the invitation to attend were also published today.
Mr Murdoch senior said that although he was not available on Tuesday, he was "fully prepared" to give evidence to the judge-led inquiry announced by David Cameron yesterday.
"I will be taking steps to notify those conducting the inquiry of my willingness to do so," he wrote.
"Having done this, I would be happy to discuss with you how best to give evidence to your committee,” Murdoch wrote, the Telegraph reports.
Mr Murdoch junior offered to attend the committee on August 10 or 11. "Naturally if neither of these proves suitable, I would be willing to consider any alternative dates you suggest,” he added.
The MPs released a statement explaining the decision to use the summons.
They said they have made it clear that “all three should appear to account for the behaviour of News International and for previous statements made to the committee in Parliament, now acknowledged to be false."
In her acceptance of the invitation, Ms Brooks said that she "welcomed the opportunity" to give evidence, reports the Telegraph.
However, she added that she might refuse to answer detailed questions about allegations of phone hacking by the newspapers because it might prejudice the ongoing police investigations.
Earlier today, Deputy Prime Minister Nick Clegg said that Rupert Murdoch must appear before MPs if he was to demonstrate “any shred of responsibility” over the crisis, reports the Telegraph.
