Multiple diplomats put the veteran well ahead of other hopefuls -- including Estonian premier Kaja Kallas and Latvia's top diplomat Krisjanis Karins -- jostling to take over from the alliance's current boss Jens Stoltenberg next year.
A successor for Stoltenberg -- who has had his decade-long tenure extended twice in the face of Russia's war on Ukraine -- is expected to be announced before a July summit in Washington.
After ruling himself out for the NATO post in previous years, Rutte, 56, is now available following his surprise resignation this summer.
Last month, he told Dutch media that running the alliance was a "very interesting" job and he would be open to the prospect if it came his way.
A familiar figure on the European stage after 13 years running the Netherlands, the Dutch stalwart is already favoured by NATO heavyweights the United States, Britain, France and Germany, diplomats say.
"He is a candidate for secretary general of NATO. He has made it clear that he's available and there's broad-based support for him," said a diplomat at the alliance.
Some supporters want to wrap up his nomination soon to avoid the NATO job getting put in the mix with EU top positions up for grabs after an election next June.
But there is likely still some frantic haggling ahead, and others warn it is not a done deal yet with possible opposition coming from awkward allies Turkey and Hungary.
One potential stumbling block for Rutte could be the situation he leaves behind in the Netherlands where a victory for far-right Geert Wilders has sent shockwaves across Europe.
"If you come from a wreck, it may be more difficult to make the argument," said a diplomat from a second NATO country.
"If you look at other front-runners before, they've often come up short in the end. Let's wait and see."
- Wishlist -
During discussions on a potential replacement for Stoltenberg in previous years, various NATO allies had laid out their wishes for the next alliance chief.
Some wanted to choose a woman to run NATO for the first time and countries on the eastern flank closer to Russia were hoping to get someone from their region.
Estonia's Kallas does meet those criteria but is seen as too hawkish towards Moscow by some to the west.
Another ask has been to appoint a leader from a country that meets NATO's goal of spending two percent of their GDP on defence.
The Netherlands did not reach that goal during Rutte's long tenure, but it has promised to next year and his backers say that shows his commitment.
Rutte's government has also taken a prominent role in supporting Ukraine, this month pledging another two billion euros and leading the push to give Kyiv F-16 fighter jets.
He would become the fourth Dutchman to head the NATO alliance, adding to arguments from some that the alliance isn't moving beyond its comfort zone.
But supporters insist he has a full awareness of the dangers posed by Russia.
His years in power were scored by the killing of 196 Dutch nationals when a missile investigators say was supplied by Moscow shot down a passenger jet over Ukraine in 2014.
- Handling Trump? -
Figuring in the thinking for some allies in Europe is also the spectre of a return to the US presidency of Donald Trump next year.
Trump reportedly mulled pulling key power the United States out of the alliance during his term and harangued other members to up their spending.
Stoltenberg managed to talk him down and was dubbed a "Trump whisperer" for his handling of the volatile former reality TV star.
Rutte was not afraid of talking straight to Trump and even contradicted him publicly on a White House visit over a possible US-EU trade deal.
The Dutchman's backers say his long pedigree finding compromises as a statesman should stand him in good stead.
Those less convinced argue it might be easier to keep Trump on side with a NATO leader who has spent bigger on defence.
"Trump during his first term was very much focusing on the necessity for all allies to contribute financially," said a third NATO diplomat.
"From that perspective somebody who has demonstrated clear commitment to this defence investment pledge is an asset."
Stoltenberg himself told AFP on Monday that Rutte was a "friend and good colleague".
"He is a capable politician with a lot of experience as prime minister," Stoltenberg said.
"But it's not for me to decide who's going to be my successor."
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