THE Cabinet will discuss the Government response to accusations of garda mismanagement of serious cases at its meeting on Tuesday.
Mr Kenny's officials are examining the allegations made by garda whistleblower, Sergeant Garda Maurice McCabe.
Labour remains keen for the public to be reassured that the issues are being handled appropriately and an independent inquiry is still on the table as an option.
Justice Minister Alan Shatter is completing a review of correspondence between his department and the whistleblower, going back several years.
But a leaked letter from the Department of Justice to Sergeant McCabe from December 2012 says the allegations were all dealt with. The investigation was deemed by the Garda Commissioner to have been "efficiently and speedily" carried out.
This weekend, ministers are again anxious for Mr Shatter to clear up the controversy.
"Shatter is going to have to solve this, he doesn't have very many friends in high places, he doesn't have too many in low places either," a Fine Gael minister said.
"Our concern is that the issue may sweep into Labour, if that happens and they get uneasy, then neither the Taoiseach nor Mr Shatter will be in control of the ball."