Rupert Murdoch and Rebekah Brooks have been called to appear before a parliamentary select committee next week as claims over phone hacking spread to other News International papers.
MP John Whittingdale had said on Tuesday that all three would appear, but later retracted the statement and said that it was now unclear if they would agree to questioning.
MP Therese Coffey said the Department of Media And Culture had invited the News Corporation chairman and former Sun Editor to appear before the Commons culture select committee next Tuesday.
News International said they were aware of the request and that "senior executives" would "cooperate" but did not elaborate.
If the invitations are declined, the committee could move to a summons stage, Coffey said, but added that the power does not apply to foreign nationals. Murdoch is a US citizen.
The move comes after Jeremy Hunt, the Culture Secretary, said he would refer Murdoch's proposed takeover of BSkyB to the Competition Commission. News Corp withdrew its offer to spin-off Sky News as part of its takeover deal on Monday.