However, the proposal stipulates that any payment must be entirely voluntary and cannot be imposed by force.
It would also require approval from the United Nations, according to a report by The Guardian.
Meanwhile, tensions between the United States and Iran over the security of the waterway remain at a critical level.
Following calls for retaliation during the funeral of Iran's late Supreme Leader Ayatollah Ali Khamenei, US President Donald Trump warned that Iran would face complete destruction.
Washington has insisted that Tehran provide a public guarantee to keep the Strait open to international shipping.
In an effort to ease the crisis, Oman has proposed a voluntary fee model consistent with international maritime law.
Iranian Foreign Minister is scheduled to visit Oman for talks on the proposal.
