A proposal by the Taoiseach to install Independent Roscommon-Galway TD Denis Naughten as the leas ceann comhairle has been rejected by other parties.
Deputy Naughten had ran for the position of ceann comhairle earlier this year but was defeated by Fianna Fail's Sean O'Fearghail.
The Sunday Times reports that the Taoiseach's proposal of Deputy Naughten for the role came following a request from O'Fearghail for the position to be filled.
O'Fearghail fears that, in the absence of a ceann comhairle or Leas Ceann Comhairle, a constitutional commission would be unable to function.
The three members of the constitutional commission are the ceann comhairle, the chief justice and the Seanad cathaoirleach, who will be appointed once a government is formed and the sitting Taoiseach nominates the 11 remaining senators to the second house.
The commission substitutes for the President and has been used in the past to dissolve the Dail and pass acts into law while sitting Presidents were overseas.