As Moscow's closest EU ally despite its invasion of Ukraine, Orban is increasingly stoking fears of a war between the West and Russia, which he blames on Brussels and NATO.
The nationalist premier recently also suggested that he would like to "redefine" the position of Hungary in the alliance to prevent any participation in operations "outside NATO territory".
Stoltenberg and Orban are to hold a joint press conference around 10 am (0800 GMT).
Stoltenberg, who has been touring NATO members, is trying to hammer out a plan to be announced at a summit in Washington next month for NATO to play a bigger role in coordinating weapons deliveries and training for Kyiv's forces.
Hungary has objected, claiming it could drag the alliance into the war with Russia. It has already refused to supply arms to Ukraine.
NATO officials and diplomats say that Budapest -- one of NATO countries friendliest to Moscow -- is being offered an "opt-out" that would mean Hungary would not be required to participate in any way.
Hungary would also likely be left on the sidelines of efforts by Stoltenberg to get NATO members to pledge to keep supplying at least support worth 40 billion euros ($43 billion) a year to Ukraine for as long as it takes.
- Increasing frustration -
Diplomats from its NATO allies are getting increasingly frustrated that Budapest -- which has already opposed helping Kyiv at the EU -- is now also threatening to block efforts by the US-led alliance to increase support for Ukraine.
One diplomat said that "in recent months especially" Hungary's opposition had become a growing issue inside the alliance.
But another diplomat was still optimistic that Stoltenberg would be able to strike a deal with Orban allowing Hungary to "constructively abstain" from NATO's plans to play a bigger role in coordinating the delivery of weapons to Ukraine.
"There is a landing zone," the diplomat said, speaking on condition of anonymity.
NATO has so far avoided being directly involved in weapons deliveries to Ukraine, for fear it would move it closer to conflict with Russia.
Instead, it has left it to Kyiv's main backer, the United States, to coordinate arms sent by alliance members.
Officials and diplomats say the reason for NATO to take more of a role now is to try to ensure deliveries could continue even if Republican presidential candidate Donald Trump was re-elected president and pulled the plug on US support.
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