The planned debate next week will see parties and TDs discuss the Esat mobile phone licence inquiry, with time set aside over two days to discuss the damning report.
But opposition TDs claim Mr Kenny has gone back on a promise he made to make members of the original cabinet who signed off on the licence deal available for questioning.
Party whips agreed the agenda for the Tuesday and Wednesday debate yesterday evening.
But out of the near seven hours set aside to discuss the report over the two days, only one hour has been made available to directly question a government minister.
Communications Minister Pat Rabbitte is set to take questions between 6pm and 7pm next Wednesday, but Sinn Féin said it is frustrated that the Taoiseach himself will not be the one being quizzed about the report during the debate.
Sinn Féin had proposed that more time be set aside on Thursday for questions and answers over the report but the Government whip rejected the proposal.
This week the Taoiseach said that the six members of the 1995 government that approved the licence, who are currently at Cabinet, would be made available for questioning.
Sinn Féin whip Aengus O’Snodaigh last night said the opposition party was not happy with the arrangements.
No motions have been set down for the debate over the endorsement of the report.
Mr O’Snodaigh also claimed that essentially it would just be a series of speaking slots for members, with little time for questioning.
“Enda said he would be available for questions, but instead it will just be Pat Rabbitte for one hour,” said the Sinn Féin party whip.