The Red C poll for the Western People shows Mr Kenny’s running mate Michael Ring topping the poll with 21%, just one point ahead of Mr Kenny who is on 20%.
While both would easily be elected on the first count on these figures, their surpluses would not transfer in sufficient numbers to their two running mates, Michelle Mulhern in Ballina or new Mayo football manager John O’Mahoney, who attract disappointing support levels of 5% and 4% respectively.
The poll, to be published in today’s Western People, was conducted face-to-face, using mock ballot papers, with a representative sample of 511 people in Mayo.
Another significant finding suggests independent TD Jerry Cowley could also be in trouble. He came second in 2002 with 14% of the votes but his support has now fallen to 8%, according to this poll.
In contrast, former FF and now independent TD, Beverly Flynn, is on 11% and is likely to attract enough transfers along geographical lines to retain her seat.
There is also good news for Fianna Fáil. Its North Mayo candidate Dara Calleary has shown up strongly. He is on 11%, the same level as the party’s sole sitting TD John Carty. If these results were repeated on polling day, both would be elected.
The other Fianna Fáil candidate Frank Chambers is on 4%, one ahead of
Gerry Murray (SF). Harry Barrett of Labour is on 1%.
And a separate poll conducted in Galway West indicates that Fine Gael may be struggling to retain its single seat in the constituency.
The poll was conducted by TNS-mrbi for Raidió na Gaeltachta. It suggests a gain for the Green Party and the almost unthinkable prospect of neither Fine Gael nor the PDs winning a single seat between them.
The poll shows the two standard-bearers for Fianna Fáil, Eamon Ó Cuív and Frank Fahey will be comfortably elected, with Mr Ó Cuív winning a massive 27% of first preferences.
With almost 47% of support, Fianna Fáil would be very close to winning a third seat in the constituency but would need to manage its vote to lift third candidate Michael Crowe.
Green Party mayor of Galway Niall Ó Brolcháin and Labour’s Michael D Higgins are both on 11%, which poll analysts say will be enough to secure both a seat. Former Labour councillor Catherine Connolly is attracting support of 3% and will not pose a threat.
The results suggest a tense three-way battle for the final seat between Fine Gael, Fianna Fáil and the PDS. Fine Gael TD Padraig McCormack is on 7% with Fidelma Healy Eames on 5%.
With Noel Grealish, PD TD on 8%, it suggest a three-way tussle with Mr McCormack and Mr Crowe for the seat.