Tanaiste Simon Coveney has been in contact with Verona Murphy and a number of other independent TDs as Fine Gael seeks to attract further support for a coalition government with Fianna Fail and the Greens.
Coveney reached out to members of the Regional Independent Group in a series of phone calls on Friday evening. Members of the group, which includes controversial TDs Michael Lowry and Noel Grealish, expect to take part in talks about joining the government within the next two weeks.
Murphy, a TD for Wexford who fell out with Fine Gael over comments about migrants when she ran for the party in a by-election last year, said she had a "very good relationship" with Simon Coveney.
She spoke to him on Friday about the progress being made in the government formation talks and did not rule out being involved. "If they come up with a programme for government with the Greens, then we need to see that," she said.
Murphy said a key issue for her would be moving Dublin Port to Rosslare, which is in her constituency, to help reduce high nitrogen oxide emissions in the capital. "If the Greens are really serious, they'll be looking at this," she added.
Coveney's calls to Independents sparked alarm among some in the Green Party who harbour concerns over the potential involvement of controversial figures such as Lowry, who has been found guilty of tax offences, and Grealish, who was widely criticised last year for claiming African migrants "sponge off the system". Neither returned calls yesterday.
A Green Party source said the involvement of some TDs would be a "hard pill to swallow".
A spokesman for Simon Coveney said: "The Tanaiste told many of the Oireachtas colleagues he'd met since the election that he'd keep in contact with them and he's done that. The government formation talks are going well."
Waterford TD Matt Shanahan and outgoing junior minister Sean Canney said they were both interested in participating in talks.
The group's co-ordinator, Denis Naughten, did not return calls. Other members are Independent TDs Peter Fitzpatrick and Cathal Berry and Aontu's Peadar Toibin who has ruled out joining the government.
Fianna Fail, Fine Gael and the Greens discussed healthcare yesterday. The parties are now aiming to have a government in place by the third week of June, after allowing two weeks to ballot members. It is hoped the programme for government can be agreed before June 7, the date when nominations for the Green Party leadership close.
The talks were disrupted last week when it emerged that Green Party members wanted deputy leader Catherine Martin to replace Eamon Ryan as leader. She said was giving "serious consideration" to challenging Ryan.
A Fine Gael source said Ryan was "quite diminished" by the move.