According to the Daily Mail the TV chef has been invited by the US Embassy in London to apply for a visa, and would be asked by officials to supply a blood sample to prove she has no illegal substances in her system.
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The star was turned away from an LA-bound flight after checking in at Heathrow on Sunday morning.
The problem stems from the confession Nigella made during a court case back in November that she had taken drugs several times.
Despite the controversy surrounding the public trial, Scotland Yard decided not to take the confession further. But America reserves the right to ban visitors entering the country if they have admitted to drug use, even if they have not been convicted.
The domestic godess was due to fly to LA to act as a judge on TV cooking show The Taste, and she arrived at Heathrow on Sunday morning to take a British Airways flight.
But is understood that the 54-year-old star checked in and cleared security when she was told she could not fly.
The TV chef admitted she had used drugs several times during her marriage to Charles Saatchi.
"She didn't seem to say much, but she did not look happy. She could not get on the flight so she had to turn around and leave," a witness told theDaily Mail.
The mum of two is believed to have registered online for permission to travel to the States, where travellers must confirm that they have not been arrested or convicted of offences, including taking illegal drugs.
The day before her scheduled trip, Nigella posted a photo on Twitter showing her excitement at heading Stateside. "Packing for my holiday! #essentials" she wrote alongside the snap, which showed a sunhat, a tube of Colman's Mustard and a small tin of Maldon sea salt.