The Italian paper cited anonymous sources saying that Stoltenberg's candidacy was being pushed by both German Chancellor Angela Merkel and US President Barack Obama.
Stoltenberg on Tuesday refused to comment on the rumours,
"I think that it is always nice to be mentioned in various contexts, but I'm keen to answer the same now as at the other times I've been mentioned in relation to different positions or positions," he said, stressing that he would neither confirm nor deny the rumour.
Until La Repubblica's report, it was generally thought that the next appointment would go to someone from outside Scandinavia, with Italy's Foreign Minister Franco Frattini, Britain's Defence Secretary Philip Hammond, and the Polish Foreign Minister Radoslaw Sikorski all names seen as being in the running.
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Nato has been led by a European ever since it was founded in 1949, but according to NTB there are otherwise few selection rules or guidelines.