Michelle Mulherin is also likely to take one of the seats
A new poll shows Fine Gael is on course to retain three of four seats in the Taoiseach's home constituency of Mayo.
The Millward Brown poll has been published in the Irish Independent.
It involved face-to-face interviews with 502 adults at 46 sampling points in Mayo, between February 9th and 11th.
The margin of error is 4.4%.
The poll of the four seat Mayo constituency shows Enda Kenny is at 24%, followed by his party colleague Michael Ring on 23%.
Fianna Fáil's Dara Calleary is on 19%, while Sinn Féin's Rose Conway-Walsh is on 11%.
Fine Gael's Michelle Mulherin stands on 9% - with Fianna Fáil's Lisa Chambers on 8%.
Group political editor of Independent News and Media - Kevin Doyle - says the poll shows when second preferences are considered, Michelle Mulherin is likely to take the fourth seat.
"We also asked about second preferences and where the vote would go after that, and that's where Michelle Mulherin makes the big gain" he told Newstalk Breakfast.
"Over 50% of people are going to give their second preference to Fine Gael as well - so while Michael Ring and Enda Kenny are likely to get a quota on the first round of votes, there's a huge transfer over to Michelle Mulherin".
"And that should keep her ahead of - particularly - Rose Conway-Walsh, who really isn't transfer-friendly at all" he added.