Another defence lawyer, Imam Asmara Hadi, said the legal challenge had been made on the grounds that the bombers had not been properly informed that their previous appeals had been rejected.
Nengah Sanjay, a Denpasar court official, told news agency Reuters that a three-page appeal document had been lodged which would be sent to a court in Cilacap, central Java, close to the prison island housing the three men.
Legal options 'exhausted'
|Security has been stepped up across Indonesia amid fears the executions could spark more attacks [AFP]
However, state prosecutors claim the three have already exhausted all their legal options and that their 2003 death sentences must be carried out.
Indonesia's supreme court has previously thrown out requests for judicial reviews, and the constitutional court has also overruled a petition from the bombers arguing that the country's method of execution by firing squad is inhumane.
A spokesman for the attorney general's office said: "No more appeals can be accepted because the limit is only one."
Despite this, Indonesian courts have considered at least three appeals on behalf of the bombers.
Security has been tightened across Indonesia ahead of the executions amid fears their deaths will provoke further violence from members of Jemaah Islamiyah - an Islamic group the three are believed to have joined.
Revenge attacks fear
The men have publicly said they hope their deaths will spark revenge attacks.
Security has been stepped up around tourist destinations, foreign embassies and oil companies, according to the national police.
Additional guards have also been deployed to the seaport of Cilacap, the city connecting Java to the high-security Nusakambangan prison ahead of the executions.
Despite widespread fears of further attacks, International Crisis Group, the conflict resolution organisation, said the executions were unlikely to lead to more bombings because Jemaah Islamiyah has been severely weakened.
Three small bombs exploded in Indonesia's Moluccas island early on Monday but there were no casualties, local police said.