The countries involved will consider the cases individually.
Turkey has dismissed, suspended, detained or arrested tens of thousands of people since the July coup attempt.
Many have been in the military, although others are teachers, policemen, judges and journalists.
The Turkish government`s crackdown has targeted those it suspects of links to the man it believes masterminded the coup attempt - the cleric, Fethullah Gulen.
He lives in self-imposed exile in Pennsylvania in the United States and has denied any involvement.
Mr Stoltenberg said on Friday that "some Turkish officers working in the Nato command structure... have requested asylum in the countries where they are working".
German media have carried reports that some members of the Turkish military have requested asylum in Germany.
Also on Friday, the UN rapporteur on freedom of expression, David Kaye, warned of a "grim" climate in Turkey since the failed coup.
He said: "The conclusions I would say are fairly grim and reflect what I think is a deep sense of restriction on freedom of opinion and expression throughout the country."
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