He will also discuss it with congressional leaders from both the Republican and Democratic parties.
The New York Times reported Tuesday that long time Republican undocumented opponent Senator Rand Paul will now come out in favor of comprehensive reform.
His move and the work of a bipartisan group of senators on a comprehensive bill, means that prospects are brighter than for many years on the issue.
Kenny will also present a bowl of shamrock to the President at the White House to mark the official St Patrick’s Day celebrations in Washington.
In a tradition going back to 1952, the shamrock ceremony will be held in public. Up to 300 Irish American leaders will be at the White House for the annual St.Patrick’s party.
However, President Obama will cut short his usual time at the event to fly to Israel and the Middle East.
Vice President Joe Biden is in Rome at the inaugural mass for Pope Francis 1 and will also not be in attendance but will have breakfast with Irish leader Kenny on Wednesday.
Prime Minister Kenny and Obama will then speak privately about the plight of the 50,000 illegal Irish immigrants in the US.
The EU-US trade agreement currently under discussion and its potential to create jobs in Ireland will also be on the agenda as well as the Irish economy.
Kenny and his deputy Eamon Gilmore will then travel to Capitol Hill for the traditional St Patrick’s Day lunch.
Meetings to be held later in the day with senior US politicians include a sit-down with former Republican presidential candidate John McCain and Democratic senators Pat Leahy and Chuck Schumer.
The undocumented Irish will be the main topic of discussion at these meetings.
Kenny has already pitched a confident message of Ireland’s prospects for growth over the coming years according to the Irish Times report.
He said: “The Irish people have given the Government a resounding mandate to make difficult decisions and help rescue the economy.”
Labor Party leader Gilmore told the paper that he was more concerned about getting the country ‘back on its feet economically’ despite recent poor showings for his party in opinion polls.
He said: “We are not going to flinch from this task. The government is two years into a five-year term and plans to stay the course to get the country through its biggest economic crisis since the foundation of the state.”
Gilmore added that the St Patrick’s Day visits to the US and other parts of the world were part of this plan.
He added: “Government ministers are here to try to encourage investment, trade and exports, and to secure and create Irish jobs.”