A three-judge panel at the Supreme Court in Jakarta unanimously rejected Lindsay Sandiford's efforts to have the sentence lifted.
The court agreed with the decision of Bali's Denpasar district court, which issued the death sentence, and the island's high court, which rejected her first appeal.
Sandiford, 56, from Cheltenham, was sentenced to death by firing squad after being found with cocaine worth an estimated £1.6 million as she arrived on the Indonesian island on a flight from Bangkok, Thailand, in May last year.
The Foreign Office said it could not comment until the details had been formally verified.
A Foreign and Commonwealth Office spokesman said: "We are aware of unconfirmed reports that the decision of the Indonesian Supreme Court has been announced. We are seeking confirmation of the decision from the Indonesian Supreme Court.
"We will continue to provide consular assistance to Lindsay Sandiford and her family at this difficult time."
She was sentenced in January.
Balinese police claim Sandiford was at the centre of a drugs-importing ring involving three other Britons.
She denies the allegations, claiming she was forced to transport the drugs to protect her children, whose safety was at stake.
Sandiford, originally from Redcar, Teesside, was arrested at Bali's airport after 10.6lb (4.8kg) of cocaine was found in the lining of her suitcase during a routine customs check.
She was later accused of damaging the image of Bali and received the death sentence following her trial. The penalty was imposed despite prosecutors asking only for a 15-year jail term.