Clare's only Fine Gael TD, Mr Donal Carey, is expected to come under pressure from the party leader to have his name added to the ticket after he failed to be selected at a convention on Thursday night.
Up to 1,000 party supporters, including 620 delegates, attended the first contested selection convention in 19 years, which had four candidates seeking nomination to two positions.
The Clare constituency is key for Mr Michael Noonan, in his strategy to gain extra seats in marginal constituencies. Clare is dominated by Fianna Fβil whose three TDs are Ms S∅le de Valera, the Minister for Arts, Heritage, Gaeltacht and the Islands, Mr Tony Killeen and Mr Brendan Daly.
Thursday night's surprising result returned Sen Madeleine Taylor Quinn and the new Dβil challenger, county councillor Mr Pat Breen, a former county chairman of the party, as candidates. The thinking is that a second seat would best be secured by Mr Carey having a running mate.
After the vote, Mr Carey, asked if he would agree to having his name added to the ticket by Mr Noonan, said he was not yet going to make up his mind. Having come through the party ranks through the democratic process, and having failed to be elected at the convention, he said he had a difficult dilemma to resolve.
On the first count, he was 60 votes short of the 206 vote quota. "That will probably be the deciding factor for me in what I do for the future," he said.
However, the director of organisation, Mr Phil Hogan TD, said there had been an expectation at national level that three candidates would be selected at the convention.
"I would encourage Deputy Carey to reflect carefully about contesting the election and not to rush to any hasty judgment by ruling it out."
In his address before the result, Mr Noonan said the election in Clare would be fought around the future of Shannon Airport.
"We must campaign on the basis of Shannon Airport and how essential that is to the Midwest, down the whole west coast of Ireland, how essential Aer Lingus is to us, how essential the tourist industry is to us in this part of the country. Very quickly, the Government must bring forward a policy on the future of Shannon Airport."