The latest political opinion poll shows that 40% of voters would like to see Labour leader Eamon Gilmore as the next Taoiseach.
Some 29% favour Fine Gael leader Enda Kenny, while just 18% would choose current Taoiseach Brian Cowen.
The Red C/Sunday Business Post survey also shows a jump of 5% in support for Labour, bringing them up to 27%
Fianna Fáil has remained the same on 24%, while Fine Gael is well ahead on 33%.
The Green Party is set to lose all of its seats in the next election, if current trends continue.
The survey shows that support for the Green party has fallen by 3% to 2%, from 5%.