Ahead of a summit of leaders in Lithuania's capital Vilnius next month, NATO's 31 countries are now discussing finding a successor to replace him as the alliance's secretary general.
Stoltenberg -- who has been at the helm of the Western military alliance since 2014 -- already had his tenure prolonged a year, to October, in the wake of Russia's invasion of Ukraine in February 2022.
Danish Prime Minister Mette Frederiksen has emerged as a possible frontrunner to succeed him. British Defence Minister Ben Wallace has also thrown his hat in the ring.
But there is so far no consensus on a clear pick among NATO members, and diplomats are increasingly talking up the chances of Stoltenberg being asked to stay on.
Stoltenberg, 64, reiterated that he does not have "any intention of seeking an extension", but added that the call was up to NATO members.
"When it comes to my successor that is an issue to be decided by the 31 allies," Stoltenberg said at a meeting of NATO defence ministers in Brussels.
"I'm responsible for all decisions that this alliance has to take except one, and that is about my future -- that is for 31 allies to decide."
Several diplomats from NATO countries said it seemed increasingly possible they could keep Stoltenberg in charge.
A diplomat at NATO said that it appeared the alliance was now "moving towards" an extension for Stoltenberg, up to a summit in Washington next year to mark its 75th anniversary.
"If we don't agree on a successor candidate, NATO can't be without a secretary general, and I'm of course in favour of an extension," said German Defence Minister Boris Pistorius.
- 'Doesn't sound bad' -
Frederiksen -- who has recently visited the United States, NATO's dominant power -- ticks the requirements of some European allies as a possible first female leader and from the EU.
But NATO nations on the alliance's eastern flank have been pushing for someone from their region to take the reins to underscore a tougher stance on Russia.
If she were chosen, Frederiksen would be the third successive NATO chief from Scandinavia, after Stoltenberg, a Norwegian, and Denmark's Anders Fogh Rasmussen.
Britain's Wallace has been pushed by London, but numerous allies want a former head of state or government in charge, and diplomats say France wants someone from an EU country.
There is no formal process to pick the NATO secretary general and the choice on previous occasions has sometimes been a little-mentioned choice who emerged at the last minute.
The alliance head has traditionally been from Europe.
Finnish Defence Minister Antti Kaikkonen said extending Stoltenberg's tenure "doesn't sound bad to my ears".
"Stoltenberg has done a very good work. But, of course, I'm sure that he's interested in retiring some day," Kaikkonen said.
"We'll see what kind of solution we will have."
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