David Cameron is prepared to consider ordering an investigation into Jeremy Hunt's dealings with News Corporation but not until the Culture Secretary has appeared at the Leveson Inquiry.
The Prime Minister has been resisting demands to call in his independent adviser on ministerial conduct, Sir Alex Allan, insisting it is a matter for Lord Justice Leveson's inquiry into media standards.
However, he is understood to be open to the possibility of a separate inquiry into whether Mr Hunt broke the ministerial code after the Culture Secretary has defended himself in front of Lord Justice Leveson.
The deputy chairman of the Conservative Party, Michael Fallon, said that the evidence should be "tested" at the Leveson Inquiry.
"If later on, obviously, it looks as if there's something that needs to be investigated under the ministerial code that can be done," he said.
It has emerged that Lord Justice Leveson would not rule on whether Mr Hunt broke the ministerial code.
The Culture Secretary has been accused of acting as a "cheerleader" for News Corporation's BSkyB takeover bid after the Leveson Inquiry published a raft of email exchanges between the company's chief lobbyist and Mr Hunt's office.
Mr Hunt's special adviser, Adam Smith, resigned over the matter this week.
The Culture Secretary is now facing a lengthy wait to defend himself at the Leveson Inquiry after his request for an early appearance was rebuffed.
Lord Justice Leveson has refused to bring forward his appearance so that he can answer allegations about his conduct.