The two parties are to exchange policy papers to see if there is a basis for further discussion.
However, Taoiseach Bertie Ahern has ruled out changing the Government's position on the use of Shannon Airport by US troops - an important issue for the Greens, and for a number of Independents.
Though it is not clear if the issue is a potential deal-breaker for anybody currently in the Government formation mix.
The opening of contacts between Fianna Fáil and the Greens is no great surprise, but it demonstrates once again that Mr Ahern has more options for forming a Government than Enda Kenny has.
Mr Ahern could secure a majority in coalition with the Greens, or with the PDs and a number of Independents, or even with Labour.
Mr Kenny, on the other hand, has excluded Fianna Fáil and Sinn Féin from his calculations, and therefore must secure the support of Fine Gael, Labour, the Greens, the PDs and all five of the Independent TDs.
Fine Gael insists its still in the running, but even if Fianna Fáil is not serious about a deal with the Greens, it has further complicated the situation by opening contact with them.
Earlier, Progressive Democrats President Tom Parlon said there was 'a lack of reality' about Fine Gael's belief that it can secure the numbers in the Dáil to form a Government.
