The Taoiseach will reportedly seek the views of his Fianna Fáil colleagues next month on the timing of the Dublin South byelection.
There is speculation that the vote to replace the late Fianna Fáil TD Seamus Brennan may take place on the same day as next year's local and European elections.
However, reports this morning say it could be held earlier if Mr Brennan's son, Shay, decides to put his name forward.
Fine Gael and Labour are likely to put pressure on Mr Cowen to arrange an early vote in an effort to capitalise on public disquiet regarding the economic downturn.