Stoltenberg also said he would travel to Istanbul on Sunday, having been there in September when he sought to reassure Ankara of NATO's continued support.
"Some Turkish officers working in NATO command structures ... have requested asylum in the countries where they are working," Stoltenberg told a security conference in Brussels.
"We have seen a number of changeovers in the NATO command structure where Turkish personnel has been changed," the NATO chief said.
Stoltenberg said the NATO countries concerned would make their own asylum decisions rather than the alliance headquarters in Brussels.
"We would be wrong if we started to go into that kind of legal issue; that's for the judicial system" of the countries concerned", he said.
Stoltenberg did not name the countries or say how many Turkish officers were involved.
Jonathan Eyal, an analyst with the London-based think tank Royal United Services Institute, told AFP the development could create more tensions with Turkey.
Turkish President Recep Tayyip Erdogan has accused western powers of failing to show enough support and rejected their charges that he is violating human rights with his massive post-coup crackdown.
Turkey declared a state of emergency following the July 15 coup, arresting tens of thousands in a crackdown which critics say has gone well beyond the alleged plotters to include anyone daring to criticise Erdogan.
Eyal warned the NATO chain of command could be undermined in the long term as Turkey may struggle to fill the slots with officers who may be chosen for their loyalty rather than their competence.
On Thursday, German media reported that several Turkish officers from the NATO base in Ramstein had asked for political asylum together with their families.
"There is more than one person", Paul Junker, chief administrator for the district of Kaiserslautern, told the online website of the weekly magazine Der Spiegel.
On Friday the German office for Migration and Refugees confirmed that in total 4,437 Turkish citizens applied for asylum between January and October, more than double the number for 2015.
Authorities in Greece have said eight Turkish military officers fled to the northern Greek city of Alexandroupoli shortly after the coup, but they did not appear to be serving with NATO.
Stoltenberg said he would be visiting Turkey on Sunday to attend a meeting of parliamentarians from NATO countries.
Turkey joined the US-led military alliance in 1952 shortly after World War II, at the start of the Cold War.
Its membership has traditionally been a cornerstone of Turkish foreign policy.