Bashir was convicted in March and given a 30-month jail sentence. His lawyers have argued that the court decision was based on false evidence and a fabricated police dossier.
"It's true that the Supreme Court has rejected Abu Bakr Bashir's appeal, but we have not received an official notification," said the cleric's lawyer, Muhammad Assegaf, on Saturday.
The authorities in Indonesia, the world's most populous Muslim nation, and some foreign governments say the 66-year-old cleric is the head of the al-Qaida-linked Jemaah Islamiah network operating in Southeast Asia.
"He [Bashir] feels it is an act of injustice since the very beginning. It was clearly an intervention by foreign countries," Assegaf said.
Bashir was acquitted of charges that he led Jemaah Islamiah, ordered the Bali bombings or was involved in a 2003 blast at Jakarta's JW Marriott Hotel that killed 12 people.
The verdict prompted the United States and key ally Australia to call for a review on the grounds the sentence was too lenient. The Bali nightclub blasts killed 88 Australians.
"He will continue to fight this injustice, and he rather fight in silence than having to admit that the allegations were true," said Assegaf.