It is widely believed that polling day will be on Friday 26 February.
RTÉ reports that ministers had predicted that Mr Kenny would announce his intention at Tuesday's cabinet and go to the country thereafter.
Mr Kenny has decided to allow the Irish parliament another sitting day in part to allow for an orderly dissolution.
He is aiming to become the first Fine Gael leader to be returned as prime minister.
Fine Gael ministers met for two hours on Monday night to sign off on their party manifesto.
The outgoing Fine Gael and Labour coalition, which had a huge majority, is set to lose a massive number of seats.
However, it hopes to be re-elected, arguing that at a time of economic recovery - fragile though it may be - stability is better than uncertainty.
Micheál Martin's Fianna Fáil party and Gerry Adams's Sinn Féin have said the fruits of the recovery are not being evenly distributed.
The 32nd Dáil will have 158 seats, eight fewer than the previous one, and the number of constituencies has been reduced to 40 from 43.
Fianna Fáil, the party that dominated politics in the Republic of Ireland until the 2008 economic crash, has ruled out both Fine Gael and Sinn Féin as coalition partners.
Irish Prime Minister Enda Kenny is now expected to call a general election on Wednesday.