The deployment comes as the Trump administration steps up pressure on Venezuelan leader Nicolas Maduro, doubling its bounty to $50 million earlier this month on drug charges against the leftist strongman.
The three Aegis-class guided missile destroyers are heading to the waters off Venezuela, the US source told AFP on condition of anonymity.
US media reported that Washington was also planning to send 4,000 Marines to the region.
Washington, which does not recognize Maduro's past two election victories, accuses him of leading the Cartel de los Soles ("Cartel of the Suns") cocaine trafficking gang.
The Treasury Department gave the group a special terrorist designation last month, accusing it of supporting the Tren de Aragua and Sinaloa drug cartels, which were labeled foreign terrorist organizations earlier this year.
The White House said on Tuesday that Trump would use "every element" to stop drug trafficking, when asked about the possibility of US boots on the ground in Venezuela.
"President Trump has been very clear and consistent, he's prepared to use every element of American power to stop drugs from flooding into our country and to bring those responsible to justice," Press Secretary Karoline Leavitt said.
Leavitt described the Venezuelan government as a "narco-terror cartel."
"And Maduro, it is the view of this administration, is not a legitimate president, he is a fugitive head of this cartel who has been indicted in the United States for trafficking drugs into this country," she added.
Maduro said on Monday that he would be deploying 4.5 million militia members across Venezuela in response to US "threats."
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