Aung San Suu Kyi has been detained for 14 of the past 20 years
Ms Suu Kyi's detention was extended last year, after a US man visited her house uninvited.
Critics say the junta intends to detain her until after elections this year.
Home Minister Maung Oo is reported to have made the comments about Ms Suu Kyi at a provincial town meeting four days ago.
The BBC's South East Asia correspondent Rachel Harvey says it is a measure of how tightly information is controlled in Burma that it has taken this long for the reports to filter out.
Burmese officials have hinted many times that Aung San Suu Kyi may be released, our correspondent adds, but this is the first time in recent months that a putative date has been attached to the idea.
Aung San Suu Kyi's own lawyer told the BBC he had heard the rumour but could not confirm it.
Ms Suu Kyi's detention was extended by 18 months last August, over an incident in which an American man swam, uninvited, to her lakeside home.
Burma extended Ms Suu Kyi's arrest after an intruder visited her home
Those include whether there would be conditions attached, whether her activities would be restricted and - crucially - whether the release would come before or after planned elections.
The Supreme Court is also due to deliver its verdict on a legal appeal against her current detention in the next couple of weeks.
But if the military government says she will continue to be detained until at least November, the court's decision has already been somewhat undermined, says our correspondent.
Maung Oo is also reported to have said the vice chairman of Ms Suu Kyi's political party, the National League for Democracy (NLD), will be released in February.
Tin Oo, 82, has been in prison or under house arrest for more than a decade.
Analysts say if he is released, he could have a key role in deciding whether or not the NLD participates in the elections due later this year.
No date for the poll has yet been set.
But if Tin Oo is released in February, and Aung San Suu Kyi remains in detention until November, it could indicate that the elections are pencilled in for a date sometime between the two, says our correspondent.