Rhodri Morgan has told Labour AMs he intends to remain as first minister and Welsh Labour leader "until the budget is put to bed", BBC Wales understands.
AMs are due to vote on the 2010-2011 assembly government budget on 8 December, and the party is expected to elect his successor in the meantime.
Mr Morgan has yet to make a formal announcement on his plans.
He made no comment on his departure timetable as he cut a cake to mark his 70th birthday on Tuesday.
He said he would join a "family celebration" in the evening.
Reflecting on the 10 years since his 60th birthday, he said his enthusiasm for devolution was "undimmed", and that the people of Wales were "immeasurably more confident" than a decade ago as a result of the assembly.
First Minister Rhodri Morgan was presented with a cake to mark his 70th birthday in Cardiff
Mr Morgan was asked later to clarify the timescale for his departure by Conservative AM Nick Ramsay during First Minister's Questions in the assembly chamber.
Mr Morgan told AMs: "The responsibilities of government and the resilience of government is of ultra, extreme importance and I will always have that in my mind in any decision I take".
At the Labour Party conference on Sunday he said his leadership "does not have long to run" and that he would give further details "before too long" about his departure.
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