Allowing the five to leave Iran, which could take weeks, would remove a major irritant between Washington and Tehran.
Iran has threatened retaliation against any company unloading Iranian oil from the seized tanker.
Iran’s IRGC has threatened to strike back against “those involved in offloading the cargo."
The news comes as Washington and Iran are trying to ease tensions and revive broader talks over Iran's nuclear program.
Earlier this week, Washington said it could soon offer to put armed sailors and Marines on commercial ships in the region following Iran's seizure and harassment of vessels.
The US has issued a new waiver to let Iraq pay Iran for electricity to keep Iran from forcing power cuts.
Since 2019, there has been a series of attacks on shipping in strategic Gulf waters at times of tension between the United States and Iran.
Michael McCaul, chairman of the Foreign Affairs Committee, wrote to Blinken on Friday, asking why the State Department's special envoy for Iran, Rob Malley, was placed on unpaid leave.
ABOVE THE FOLD: Iranian leadership has proven, time and time again, that negotiations and agreements are simply a cover for their master plan. Time and time again the West has played into their hands.