The move to defuse tensions follows repeated private warnings from US officials to the Iraqi government since January, sources including six militia commanders said.
Washington has told Baghdad it could target the groups with airstrikes unless it acted to disband the militias operating on its soil.
A senior Shi'ite politician close to Iraq's governing alliance, Izzat al-Shahbndar, said discussions between Prime Minister Mohammed Shia al-Sudani and militia leaders were very advanced, with the groups inclined to comply with US calls for disarmament, acknowledging the risk of being targeted.
"The factions are not acting stubbornly or insisting on continuing in their current form," he said.
The militia commanders, from groups including Kataib Hezbollah and Nujabaa, said their main ally, Iran's Revolutionary Guards (IRGC), had given them its blessing to make necessary decisions to avoid a conflict with the US and Israel.
"Trump is ready to take the war with us to worse levels, we know that, and we want to avoid such a bad scenario," said a commander of Kataib Hezbollah, the most powerful Shi'ite militia.
Later on Monday, Iraqi politician Muthal al-Alusi denied the Reuters report, calling the claims a nominal effort to protect involved politicians. He told Iran International that "in practice, the real militias have received advanced weapons, and their participation on the battlefield may be completely evident."
These militias form a key part of the Islamic Resistance in Iraq, an umbrella group claiming responsibility for numerous attacks on Israel and US forces since the Gaza war.
Prime Minister Sudani's advisor said he was committed to bringing all weapons under state control through dialogue.
Security officials said some groups had already evacuated headquarters in fear of air strikes.
While a US official expressed skepticism about the long-term nature of any disarmament, the discussions mark a potential shift amid a weakened "Axis of Resistance" for Iran.
Options for the militias' future include becoming political parties or integrating into the Iraqi army, though no deal is finalized.
The shift comes as Iraq balances its alliances with both the US and Iran, with the militias having grown significantly since the 2003 US invasion. The US had warned Iraq against revenge attacks by these groups after recent strikes on the Houthis.
