Fine Gael Minister Hildegarde Naughton has said she hopes Kate O'Connell seeks the party's nomination to run in the next general election.
The party lost the seat it held in Dublin Bay South with it's byelection candidate Cllr James Geoghegan coming second to Labour's Ivana Bacik.
The byelection came about due to former Fine Gael minister Eoghan Murphy’s departure from politics.
Ms O’Connell lost her seat in the constituency in last year’s general election.
Ms O’Connell announced in May she would not seek her party’s nomination saying it was clear she was “not the desired candidate” of the leadership while also highlighting issues within Fine Gael locally.
Like Ms O'Connell, Ms Naughton – a junior Minister at the Department of Transport – was a supporter of Simon Coveney during his unsuccessful bid to succeed Enda Kenny as party leader, with Leo Varadkar winning that contest.
On Friday, the Tánaiste rejected any suggestion that the result in Dublin Bay South would have been different if former TD Ms O’Connell had been the candidate.
He argued that Mr Geoghegan’s support matched that of Mr Murphy and Ms O’Connell combined in last year’s election and also said Fine Gael had been up against a “really strong candidate” in Ms Bacik in outlining his reasons for why the result would not have been different.
He said it was Ms O’Connell who took the decision not to put her name forward and that she didn’t seek his support or that of the local membership to run.
He said: “It is, was, and always will be” up to Ms O’Connell to seek the nomination if she wants it.
On RTÉ Radio on Sunday Ms Naughton was asked if Fine Gael would have done better with a woman candidate and she replied: "I don't think we know the answer to that."
She highlighted the level of support Mr Geoghegan got and also said it’s very difficult for Government parties to win byelections.
Asked if Fine Gael will look to Ms O’Connell to recover the seat, Ms Naughton said: “I would hope that Kate would put her name forward for convention at the next election.
"We all have to do that. I had to do it here in Galway West."
It was put to her that Ms O’Connell’s lack of public support for Mr Geoghegan would make it more difficult for her to return to the Fine Gael fold.
Ms Naughton said: “I served with Kate in the last Dáil. She has a really proven track record, a very able public representative and I would hope that she would put her name forward.
“It’s her prerogative obviously in relation to who she wants to support so it’s not up to me to say what she should or shouldn’t do.
“And I would hope that she herself will put her name forward.
“There was two seats in Dublin Bay South. I believe we can win those again and I think James has proven the Fine Gael base vote within that constituency and Dáil seats are hard fought.
“Kate knows this. We were all very disappointed that she didn’t get re-elected in the last election.
“The people of Dublin Bay South didn’t come out to vote for her.”
“I would hope that come the next election, which is a number of years away, she will put her name forward as will James or anyone else who wants to put their names forward for the party members to select their candidate.”