It follows days of speculation over when the Taoiseach intends to stand down as leader of Fine Gael.
Kenny, who has been prime minister since 2011, has said he will not lead the party into the next election due late next year.
It's very important that we wait and hear what the Taoiseach has to say.
"So I think we all look forward with interest to see what he has to say".
This seems the most likely outcome or else he may face an oust from within his own party with leading figures from Fine Gael set to cast their hats into the ring to become party leader. The situation is distracting and destabilising for...
An Taoiseach has said he would address a meeting of the Fine Gael parliamentary party on Wednesday and would not discuss the matter any more until then.
Jakarta decides: millions turn out to elect governor in religiously charged race
Image copyright AFP Image caption In his trademark checked shirt, Mr Purnama voted alongside his family on Wednesday. It is incumbent Governor Basuki "Ahok" Tjahaja Purnama's first electoral test as head of Jakarta.
Over the weekend, a clear timetable for the Taoiseach's departure from office was set out by two ministers who are expected will seek to replace him.
One of the two leading contenders to take over as leader of the center-right party said on Sunday that a new leader should be chosen after Kenny's trip to Washington for the annual meeting with the USA president to mark St. Patrick's Day on March 17.
CARGO TRAGEDY Aer Lingus to be sentenced for health and safety breaches after driver death at Dublin Airport...
In a screengrab taken on Sunday, Charlie Flanagan told the group that Simon Harris "wants out of Health", which he has since clarified was just "Sunday afternoon banter".
He said: "It was a joke which should be taken as that. I regret that it has been taken so seriously", Minister Flanagan today explained.
Minister Harris says he is "absolutely honoured to hold this position" and that "people can say what they like about me, but I would hope that even my harshest critics would acknowledge that I am doing everything that I can in this role".