Sinn Fein representatives in Offaly and Westmeath are casting their votes on Monday.
The Sinn Féin President says none of the party's councillors will be under the thumb to oppose Independent nominations to the presidency.
Offaly and Westmeath County Council are set to vote on any presidential candidate who is proposed and seconded on Monday.
Councillors Julie McCourt, and David Jones in Westmeath, and Aoife Masterson in Offaly will be given free choice when it comes to considering any independent candidate.
Mary Lou McDonald says candidates should be heard fairly:
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