The Omani proposal has regional backing, Reuters quoted the source.
The proposal is based on the Strait of Malacca, where those who use the strait voluntarily contribute to fund navigation, environmental protection and search and rescue.
Iran's Foreign Minister Abbas Araqchi discussed the Strait of Hormuz with his Omani and Saudi counterparts on Monday.
He emphasised the need to strengthen cooperation and advance joint diplomatic efforts to establish stability in the region and lift the insecurity imposed on the Strait of Hormuz due to the aggressive actions of the United States," according to Iran's foreign ministry statement.
The US abruptly suspended a campaign of air strikes against Iran over the weekend, raising hopes of a diplomatic solution that would allow shipping to resume in the Strait of Hormuz - which carried a fifth of global energy supplies before the conflict.
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