The Fine Gael front bench are set to discuss the drop in support shown in recent opinion polls at a meeting today.
One poll, showing Fine Gael and Fianna Fáil neck-and-neck, has resurrected questions about Mr Kenny's leadership.
Mr Kenny's communication skills and media performance will also be discussed, along with the expected appointment of consultant Mark Mortell to advise Mr Kenny on improving his media performances.
Meanwhile, similar issues are up for discussion in Fianna Fáil shortly.
After backbenchers called for a special meeting to discuss Mr Cowen's communication skills, a spokesperson says TDs and Senators will get to have their say at a meeting in the coming weeks.