The footage, taken at a party in Delaware earlier this month, allegedly shows Ashley Biden, 27, using a straw to sniff several lines of the drug.
An anonymous male friend of Ms Biden is trying to sell the 43-minute tape for $250,000 (175,000) through lawyers, according to several US newspapers whose reporters have viewed excerpts.
The New York Post, which did not submit a bid, said the seller's attorney claimed the film was shot with the knowledge of Ms Biden, a social worker with the Delaware Department of Children, Youth and Families.
The growing scandal provides an early test for President Barack Obama's fledgling administration, which is so far refusing to comment amid efforts to establish the authenticity of the film.
Mr Biden and his wife, Jill, were yesterday still in Chile on an official visit and had not spoken about the allegations, while calls to Ms Biden's home in Wilmington, Delaware, went unanswered.
If genuine, the film will prove a severe embarrassment for her father, a staunch anti-drugs campaigner who is credited with coining the phrase "drugs czar" for the first director of the Office of National Drug Control Policy almost three decades ago.
Since becoming a senator for Delaware in 1973, Mr Biden has pushed for harder penalties for cocaine possession and trafficking and last year sponsored a new bill aimed at curbing the smuggling of Colombian cocaine into the US in submarines.
"The drug trade is a problem we all share and one whose ultimate solution we must devise together," he said last week in an opinion piece published in leading newspapers across Latin America timed to coincide with his visit to Chile.
Earlier this month, at a White House press conference to introduce Seattle's police chief, Gil Kerlikowske, as the country's new drugs czar, Mr Biden spoke of the misery caused to the families of those who take drugs.
Meanwhile, more details of the tape emerged last night as the lawyer handling the sale, Thomas Dunlap, of Washington DC firm Dunlap, Grubb and Weaver, abruptly quit.
Mr Dunlap told ||WEBSTART||radaronline.com||WEBSTOP||, which claimed to have seen the tape, that he "did not want to be involved due to circumstances surrounding the publicity of the matter".
The website also claimed that, contrary to earlier statements, the footage was taken with a hidden camera and that Ms Biden was not aware she was being filmed.
In scenes viewed by reporters, a woman in her 20s with long brown hair takes a straw from her mouth, places it in a nostril, bends over a desk and snorts several lines of a white powdery substance.
Then she stands up and, with her back to the camera, talks to a friend. "At one point she pretty much complains the line isn't big enough, and she talks about her dad," said another lawyer representing the seller.
The New York Post said yesterday the seller, who wanted to remain anonymous because he feared arrest for his knowledge of drugs at the party, originally demanded $2 million for the tape but then dropped the asking price.
A British tabloid newspaper and an American media company have allegedly offered $225,000.
BIDEN & DRUGS
"We know we need to help keep kids away from drugs, and that's obviously not easy"
Joe Biden, earlier this month
"Just the health and economic cost alone from drug and alcohol abuse amounts to over $350 billion a year … (but there is] an even bigger cost, in human suffering – the pain and destruction that abuse brings to not only the abuser, but to the family and everyone who loves that person"
Biden, from the same speech