At least 1300 people have been killed since May after Jakarta sent in troops to put down separatists fighting for independence.
Top security minister Susilo Bambang Yudhoyono said a full cabinet meeting would be held on Thursday to take a formal decision on the extension.
"The president has agreed that during the extension (period) the integrated operation should be improved and sharpened," Yudhoyono told reporters. He said the status would likely be extended between four and six months.
The government on 19 May put Aceh under military rule for six months and launched a huge offensive involving 40,000 troops and police to wipe out the Free Aceh Movement (GAM), after peace talks collapsed.
It said at the time its "integrated operation" would also include humanitarian and law enforcement campaigns.
Yudhoyono said that during the extension the government would grant amnesty to separatists who surrender.
Senior security ministers met earlier in the day to discuss Aceh.
"An evaluation shows that targets have not been fully achieved so an extension of six months is needed," said Justice Minister Yusril Ihza Mahendra.
More than 900 separatists and 67 police or soldiers have been killed since May in the country's biggest military operation since the 1975 invasion of East Timor, the army says.
Deployment to Aceh is Indonesia's
biggest military operation since
1975 invasion of East Timor
It says more than 1800 separatists have been arrested or have surrendered.
The military also says more than 300 civilians have also died, but does not say who was responsible.
Under martial law most foreigners, including aid workers have been banned from the province, making independent confirmation of casualties impossible.
Human rights violations
Human rights groups accuse both sides of continuing rights violations. The National Commission on Human Rights has urged the government to call off the offensive and reopen peace talks.
MM Billah, head of its team monitoring Aceh, said the current offensive was not different from a bloody 10-year military operation against the separatists under Suharto from 1989 to 1998.
"Having seen the plight of civilians there, I would urge the government to end the military operation and give peace talks
another chance," Billah told a press conference last Friday.
Billah said the latest investigation by his team had concluded that "the rights abuses are continuing in Aceh."
Amnesty International said it continued to receive reports of extrajudicial executions, "disappearances", torture including rape and unlawful arrests and detention during the military emergency.