The Culture, Media and Sport (CMS) Committee asked the trio to give evidence about the phone hacking and police-payments scandals at a hearing next week.
A spokeswoman for News International, publisher of the News of the World, The Sun, The Times and The Sunday Times, could not confirm whether all three would attend the hearing.
But the company said in a statement: “We have been made aware of the request from the CMS committee to interview senior executives and will cooperate. We await the formal invitation.”
Labour MP Tom Watson said the committee wanted to ask Brooks about her knowledge of payments to the police.
He said MPs also intended to quiz James Murdoch on his involvement in “authorising payments to silence” Gordon Taylor, the chief executive of the Professional Footballers’ Association, after his phone was hacked.
Watson added that Rupert Murdoch owed an apology to the family of murdered schoolgirl Milly Dowler, whose mobile was allegedly hacked by the News of the World after she went missing in 2002.
The Labour MP told Radio 4 yesterday: “They have misled parliament, egregiously, over time, they have misled the country and they have misled their readers and I think it is incumbent on MPs to get to the facts.”
Watson, who has led calls for a full investigation into phone hacking, dismissed suggestions the ongoing police inquiry meant the committee would not be able to quiz the executives.
“As far as I know the three individuals concerned are not the subject of a criminal investigation, none of them have been arrested,” he said.
“So it is not unreasonable for us to ask them why the information their senior executives gave us in a previous parliamentary inquiry was actually untrue.”
A spokeswoman for the committee said it had submitted a “polite request” for the News International executives to appear before it.
If they refuse, MPs could choose to “compel” Brooks to give evidence, although it was unclear whether that action would be able to be taken against the Murdochs because they are not British citizens.