Lord Black is pleading the fifth amendment and refused to incriminate himself before a US Securities & Exchange Commission enquiry.
The board is now looking at whether its former chief executive should be replaced as chairman. He stood down as CEO in November. The decision is understood to hang on whether Lord Black cooperates in future with the SEC.
In another development, Lord Black has been given two more weeks to make the first payment on $7.2m (£3.97m) that the Daily and Sunday Telegraph owner received without the approval of the board. However, his lawyers are now disputing the payments plus interest.
Hollinger already faces a lawsuit from shareholders who argue that the publisher's independent board members, including former US secretary of state Henry Kissinger, stood by while Black and other executives "looted" the company of as much as $300m.
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