Reports about the talks - and who is participating in them - have been conflicting this week. Iran has said that it is negotiating with Oman mainly over maritime traffic through the strait, without US interference.
At the same time, both President Donald Trump and Secretary of State Marco Rubio claim that the United States is involved - and that negotiations are moving forward.
"We are having very good discussions," Donald Trump told Fox News on Wednesday night.
At the same time, he took the opportunity to threaten new attacks if the Strait of Hormuz is not opened "very soon."
According to Axios' sources, the proposal under discussion includes an agreement for 60 days of safe passage through the strait. The agreement could then be extended.
Donald Trump said this weekend that he had chosen to call off extensive attacks on Iran to enable negotiations.
