Almost half of voters want to see President Higgins honour his promise of serving just one term.
A Red C/Sunday Business Post opinion poll shows 48% think he should commit to his pre election promise to serve only one, seven-year term.
It comes amid growing speculation that Michael D will seek another term in office.
President Higgins, who has been a popular President and still enjoys strong support, is expected to declare his intentions in July, to prepare for an autumn campaign. A Presidential election is due by next November.
The timing of the announcement, which is expected before the Dáil rises for its summer recess and after the referendum on repealing the Eighth Amendment, is designed so that speculation about his future will not dominate the political agenda in August, which tends to be quieter than at other times.