Green MEP Grace O'Sullivan has refused to be drawn on who she would back in a party leadership contest.
Yesterday, her collegaue at the European Parliament, Ciarán Cuffe, backed Eamon Ryan for the role.
A number of councillors have indcated they want Catherine Martin to become leader.
Ms Martin says she would give serious consideration to putting herself forward for the role.
Nominations close on June 7.
Ms O'Sullivan has dismissed suggestions she is sitting on the fence.
"I am definitely not the type of person who sits on any fence," she said.
"I am someone who likes to get all of the information. I would like to know who is going to be in the contest."