Frank Flannery is said to be 'still considering his position' on the growing calls for him to appear before the Public Accounts Committee.
The Rehab director is under pressure to answer questions over claims that he was paid by the charity to lobby the government on a range of issues.
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Mr Flannery also works as a Fine Gael strategist.
The PAC has already given Rehab 12 specific questions it wants addressed after its chief executive Angela Kerins appeared before it two weeks ago.
It's expected to respond to the committee this week.