The rules for securing a nomination to run for President were "skewed" towards the main political parties and should be changed, according to the Independent MEP for Connacht-Ulster, Ms Marian Harkin.
Rather than requiring the support of 20 members of the Oireachtas, the number should be reduced to about seven. Instead of requiring the support of four county councils, there should be a set figure of councillors from throughout the State who could nominate a candidate.
However, Ms Harkin, who is also an Independent TD for Sligo-Leitrim, said she supported Mrs McAleese for a second term in the Presidency.
"She has been a good President, she has reflected well what Irish people are thinking."
Meanwhile, the joint leader of the Greens in the European Parliament, Mr Daniel Cohn-Bendit, said he would support the candidacy of Mr Eamon Ryan, if the Green Party TD secured a nomination to run for President.
Asked if he would come to Ireland to canvass for Mr Ryan, he said: "If he invites me, I will go."
However, he pointed out that his position on European issues differed somewhat from the stance of the Irish Greens.
He added that the Greens in the European Parliament were precluded by the regulations from providing funding to such a campaign.
"The answer is very simple: we can't fund with European money a national campaign."
The federation of European Green parties is holding its next conference in Dublin on November 26th-27th.
