Russia has deployed navy vessels to escort an oil tanker also being pursued by US forces across the Atlantic, CBS News, BBC's media partner in the US, reported.
The ship, which has historically transported Venezuelan crude oil - but is reporting that it is not carrying any at the moment - is currently between Iceland and the British Isles.
Bella 1 has been accused of breaking US sanctions and shipping Iranian oil. It has since changed its name to Marinera and reportedly reflagged from a Guyanese to a Russian vessel.
President Donald Trump said last month that he was ordering a "blockade" of sanctioned oil tankers entering and leaving Venezuela, a move the government there described as "theft".
Two US officials have confirmed to CBS that Russia has sent a submarine and other navy vessels to escort the tanker.
The US Coast Guard tried to board it last month in the Caribbean when it was believed to be heading towards Venezuela. It had a warrant to seize the ship over its alleged breaking of sanctions.
It has since dramatically changed course and its approach to Europe has coincided with the arrival of around 10 US military transport aircraft as well as helicopters.
Russia says it is "monitoring with concern" the situation around the ship.
Two US officials told CBS News earlier on Tuesday that American forces were planning to board the ship, and that Washington preferred to seize it rather than sink it.
On Tuesday, the US military's Southern Command posted on social media that it "remains ready to support our US government agency partners in standing against sanctioned vessels and actors transiting through this region.
"Our sea services are vigilant, agile, and postured to track vessels of interest. When the call comes, we will be there."
Before any US military operation was launched from the UK, Washington would be expected to inform its ally.
For now, the UK Ministry of Defence says it will not comment on other nations' military activities.
The US officials quoted by CBS suggested that America could mount an operation like one conducted last month when US Marines and special operation forces working with the Coast Guard seized The Skipper, a large crude oil tanker flagged out of Guyana, after the vessel left port in Venezuela.

BBC Verify has been monitoring the latest reported location of the oil tanker Marinera. According to AIS location data from ship-tracking platform Marine Traffic, its reported location as of Tuesday morning is in the North Atlantic Ocean, about 300km (186 miles) south of Iceland's shoreline.
Past AIS tracking data for the vessel suggests it travelled north past the western coast of the UK over the past two days.
Under international law, vessels flying a country's flag are under the protection of that nation but Dimitris Ampatzidis, senior risk and compliance analyst at maritime intelligence firm Kpler, told BBC Verify changing the ship's name and flag might not change much.
"US action is driven by the vessel's underlying identity [IMO number], ownership/control networks, and sanctions history, not by its painted markings or flag claim," he said.
Ampatzidis added that changing to the Russian registry might cause "diplomatic friction" but would not stop any US enforcement action.
"At present, our vessel is sailing in the international waters of the North Atlantic under the state flag of the Russian Federation and in full compliance with the norms of international maritime law," Russia's foreign ministry said.
"For reasons unclear to us, the Russian ship is being given increased and clearly disproportionate attention by the US and Nato military, despite its peaceful status," it said.
"We expect that Western countries, which declare their commitment to freedom of navigation on the high seas, will begin adhering to this principle themselves."
The potential stand-off over the oil tanker comes days after the US shocked the world with the Maduro seizure from the capital Caracas. It bombarded targets in the city during the operation to extricate him and his wife on suspicion of weapon and drug offences.
With additional reporting by Kayleen Devlin, BBC Verify Senior journalist