A November release for Aung San Suu Kyi would come a month after many observers believe Myanmar will hold its first parliamentary elections in two decades.
The government has said the vote is a key part of what it says is a "roadmap to democracy, but critics say the plan will only reinforce military rule.
No firm date has yet been set for the election.
'Free and fair'
Aung San Suu Kyi has been held in jail or under house arrest for 14 of the past 18 years and most observers believe the government is keen to keep her in detention until after the election.
The three sources, who requested anonymity, said Maung Oo made the announcement attended by several hundred people in Kyaukpadaung, a town about 565km north of the former capital, Yangon.
He reportedly also said that the government would pursue an international-style market economy after holding "free and fair" elections.
|Myanmar's military has said it will hold 'free and fair' elections sometime this year [EPA]
Aung Zaw, editor of the Thailand-based magazine Irrawady
, a publication that reports on Myanmar affairs, said it was difficult to know whether to believe the comments or not.
But he said that a minister of the standing of Maung Oo "wouldn't dare" to make such an announcement on a figure like Aung San Suu Kyi without the backing of senior leaders.
"I think he has some kind of backing from the top leaders in Burma," Aung Zaw said, using the former name for Myanmar.
Last year Aung San Suu Kyi's house arrest was extended for a further 18 months after she was found guilty of breaking the terms of her detention by allowing an uninvited American man to stay at her home.
Earlier this month opposition lawyers launched a supreme court appeal against her sentence, saying it was unlawful because it was based on a 1974 constitution that is no longer valid.
A verdict had been expected last week, but the court has made no announcement.
The NLD, led by Aung San Suu Kyi, won a landslide victory in Myanmar's last election held in 1990.
But the results were never honoured by the military which has ruled Myanmar since 1962.
The NLD has not yet said whether it will participate in the upcoming vote.
Speaking to Reuters Khin Maung Sw, a senior party official, said it was crucial Suu
Kyi and Tin Oo were released before the election.
"The most important thing is they must be freed in good time so that they can work for national reconciliation," he said.