The White House's nominee to become chairman of the Joint Chiefs of Staff, General Mark Milley, said Washington was attempting to put together a coalition "in terms of providing military escort, naval escort to commercial shipping."
"I think that that will be developing over the next couple weeks," Milley told the Senate Armed Services Committee.
Tensions in the Gulf have increased in the past few weeks, with Iran's economy in free fall following the re-imposition of US sanctions after President Donald Trump pulled out from a 2015 international agreement to curb Iran's nuclear program.
The rapid chain of events further complicates Britain and other European allies' efforts to salvage the 2015 JCPOA nuclear agreement despite the US withdrawal.
Milley's statement came after London accused Tehran on Thursday of deploying three military vessels to "impede the passage" of a 274-meter (899-foot) BP tanker, the British Heritage.
"We are concerned by this action and continue to urge the Iranian authorities to de-escalate the situation in the region," a Downing Street spokesman said.
Iran's menacing of the BP supertanker on Wednesday appeared to be in retaliation for Britain's seizure of the Iranian Grace 1 tanker off Gibraltar on July 4.
Iran's Revolutionary Guards denied involvement in the British Heritage incident but said the United States and Britain would "strongly regret" British detention of the fully-loaded Iranian tanker off Gibraltar for violating sanctions on Syria, allegedly the planned recipient of its cargo.
Washington and Riyadh previously blamed Iran for allegedly using limpet mines to blow holes in Gulf-area ships in May and June, and Trump came close to ordering an attack on Iran in retaliation.
Officials in Britain and France would not confirm the discussions on a tanker escort operation.
Both, like the United States, maintain a constant naval presence in the Gulf. But London and Paris have been reticent to join in Washington's "maximum pressure" campaign against Iran to force it to pull back on its involvement in conflicts in Syria, Iraq and Yemen.
British media reported that the possible deployment of more Royal Navy ships to the region was "being looked at" in the aftermath of the newest incident.
But in France, a government official told AFP that they were not planning for the moment to expand their presence in the Gulf.
"France is on a course of de-escalation," the official said.
"Sending additional military assets to the region does not seem useful to us."
A joint effort would reprise the 1987-1988 US-led operation to protect Kuwaiti oil tankers from Iranian attacks during the Iran-Iraq war.