Several members of the Kennedy family are due to attend the official opening of a new €1.5m visitor centre and associated events.
Government officials and the US Embassy have informally discussed the prospect of Mr Obama coming to Wexford for the occasion.
"The feelers have gone out. It's at a sensitive stage and nothing's official yet," a senior government source said.
"The fact that the dates are so close together has been noted on all sides. It's on the table for discussion. It's being looked at both here and on the US side," another source said.
It came as Mr Obama swore to protect and defend the US constitution in a massive public celebration of American democracy yesterday, marking the second inauguration of the country's first black president.
The G8 summit takes place on June 17 and 18, while the Kennedy commemorations are scheduled for June 22. Kennedy's daughter, Caroline Kennedy, an author and attorney, and his sister, Jean Kennedy-Smith, the former US Ambassador, are already confirmed to attend.
Congressman Joe Kennedy's attendance is also a possibility.
A formal invitation has not been issued to Mr Obama and both sides are only sounding out the possibility at the moment.
"If the president's officials express an interest, there is nothing planned that couldn't be brought forward to facilitate his schedule," he said.
No movement on the question of checking Mr Obama's schedule has happened yet because the White House was focused on yesterday's presidential inauguration.
Diplomatic protocol would dictate that Taoiseach Enda Kenny won't invite Mr Obama until he is sure of a positive answer.
But Mr Obama's guaranteed presence in Northern Ireland for two days provides the Government with the best opportunity to get him to make a visit to the country again, following his whistlestop tour of Dublin and Moneygall, Co Offaly, in June 2011.
Mr Obama's participation would add to the prestige of the commemoration events, which already has a VIP guest list of Kennedy family members.
The most recent meeting on the events took place last Friday and was attended by officials from the US Embassy, the Department of Foreign Affairs, the Department of the Taoiseach, the government chief whip's office, the Office of Public Works and Wexford County Council.
New Ross is the ancestral home of the Kennedys. Kennedy's great-grandfather, Patrick Kennedy, boarded a famine ship from the quay in the town to emigrate to America in 1848.
Kennedy himself paid an emotional visit to New Ross on June 27, 1963.
The Office of Public Works is currently building a new €1.5m visitor centre at the Kennedy homestead, due to be completed by June, to mark the 50th anniversary of Kennedy's visit.
Also being unveiled is an eternal flame, dedicated to emigrants on the quayside in New Ross.