According to NATO rules, it is necessary to decide who will be the secretary general "by consensus", meaning Rutte still has to get the backing of all the remaining countries.
The official said the discussions are "not final," but added: "There is growing momentum behind his candidacy."
Pressure is mounting on NATO members to approve Rutte before the leaders' summit in Washington in July. He would replace Jens Stoltenberg, who has led NATO since 2014.
United States Ambassador to NATO Julianne Smith said last week that the allies should aim to "complete the selection process probably in the first quarter of this calendar year."
Another senior NATO official confirmed the number of countries that still need to support Rutte, saying that around 10 are still reluctant to vote in favor.
"We will continue to listen to your questions and concerns," the first official said. "And we encourage... the Dutch mission in NATO to answer those questions."
