The Reuters news agency was told of the apparent development - said to be a key indicator of Russia’s military preparedness - by three US officials, speaking on condition of anonymity,
It comes amid growing warnings from the West that Russia could be preparing for a new invasion of Ukraine as it masses more than 100,000 troops near its borders.
These warnings have included President Joe Biden’s prediction that a Russian assault was likely and U.S. Secretary of State Antony Blinken's remarks that Russia could launch a new attack on Ukraine at “very short notice”.
The Pentagon has previously acknowledged the deployment of “medical support” as part of Russia’s buildup. But the disclosure of blood supplies adds a level of detail that experts say is critical to determining Russian military readiness.
“It doesn’t guarantee that there's going to be another attack, but you would not execute another attack unless you have that in hand,” said Ben Hodges, a retired U.S. lieutenant general now with the Center for European Policy Analysis research institute.
The Russian Defence Ministry did not immediately respond to a request for comment.
A White House spokesperson did not immediately comment on any Russian movement of blood supplies but noted repeated public US warnings about Russian military readiness.
The Pentagon declined to discuss intelligence assessments.
The three US officials who spoke about the blood supplies declined to say specifically when the United States detected their movement to formations near Ukraine. However, two of them said it was within recent weeks.
Russian officials have repeatedly denied planning to invade. But Moscow says it feels menaced by Kiev’s growing ties with the West.
Eight years ago it seized Crimea and backed separatist forces who took control of large parts of eastern Ukraine.
Russia’s security demands, presented in December, include an end to further Nato enlargement, barring Ukraine from ever joining and pulling back the alliance’s forces and weaponry from eastern European countries that joined after the Cold War.
Mr Putin said on Friday the US and Nato had not addressed Russia's main security demands in their standoff over Ukraine but that Moscow was ready to keep talking.
Mr Biden has said he will not send US or allied troops to fight Russia in Ukraine but told Ukrainian President Volodymyr Zelensky in a phone call on Thursday that Washington and its allies stand ready to respond decisively if Russia invades the former Soviet state, the White House said.
The US and European allies have said Russia will face tough economic sanctions if it attacks Ukraine.
Western countries have already imposed repeated rounds of economic sanctions since Russian troops seized and annexed Ukraine’s Crimea peninsula in 2014.
But such moves have had little impact on Russian policy, with Moscow - Europe’s main energy supplier - calculating that the West would stop short of steps serious enough to interfere with gas exports.