The condemned group includes Australians Andrew Chan and Myuran Sukumaran, Filipino maid Mary Jane Veloso and prisoners from Ghana, Brazil, Nigeria and Indonesia.
French national Serge Atlaoui's execution has been delayed while a court considers a legal challenge.
Indonesian President Joko Widodo denied all 10 prisoners' petitions for clemency in late 2014.
Australians Chan and Sukumaran --
members of the "Bali Nine" smuggling ring
who were convicted for their role in a failed 2005 heroin smuggling plot -- tried to challenge Widodo's decision this month but lost an appeal for the State Administrative Court to hear their case.
Their attorneys filed another review at the Constitutional Court, but a spokesman for the attorney general's office told CNN on Monday that their legal options had been exhausted.
"We do not have to wait for the constitutional review case filed by the Australians. The execution will go ahead as planned," spokesman Tony Spontana said.
Spontana confirmed Sunday that the prisoners had been given notice that a firing squad could execute them after 72 hours.
It was possible that the executions would take place Tuesday, he told CNN on Monday "but only the attorney general has the authority to decide or announce that."
The Australian government has appealed for clemency for Chan and Sukumaran, unsuccessfully proposing a prisoner swap with Indonesia as a way to avoid their deaths.
In a statement Sunday, Australian Foreign Minister Julie Bishop said the men had been rehabilitated and were "genuinely remorseful."
"Nothing can be gained and much will be lost if these two young Australians are executed. I again respectfully call on the President of Indonesia to reconsider his refusal to grant clemency. It is not too late for a change of heart," she said.
'The judicial process is over'
Edre Olalia, an attorney for Veloso, told CNN on Sunday that Veloso had telephoned her sister on Saturday and said her execution would take place within 72 hours.
According to her attorneys, Veloso unknowingly carried drugs into Indonesia and was set up by members of a drug syndicate.
Philippine President Benigno Aquino has appealed for clemency in Veloso's case, and Spontana said that Indonesian Foreign Minister Retno Marsudi had spoken to the attorney general about the case.
"The attorney general explained to her that in Mary Jane's case, the judicial process is over. Her second judicial review was rejected by the Sleman court today," Spontana said, referring to a district court in Yogyakarta, Indonesia.
"We hope that when the Philippine government receives the message, it will understand that this is the legal process in Indonesia.
"We are not at war with them, we are at war with our country's drug problem. We respect our relations with our ASEAN (Association of Southeast Asian Nations) neighbors, but we should also respect the principles of noninterference in each other's internal affairs," he said.
War against drugs
Indonesia's President reiterated that message when asked about Veloso during an interview Monday with state-owned television station TVRI.
"Narcotics is damaging our nation's youth. It should be explained -- the press should explain -- that every day 50 of our young people die every day because of drugs. That's 18,000 per year," Joko said. 'We are serious in our war against drugs."
Spontano said that Atlaoui, the French national, had filed the same case as previously put to Indonesia's State Administrative Court by Australians Chan and Sukumaran. "They lost that case," he said.
The Frenchman could be executed separately, he said.