Obama used a landmark encounter with Thein Sein, Myanmar's prime minister, at a regional summit in Singapore on Sunday to demand freedom for the Nobel peace laureate.
Aung San Suu Kyi has been under detention for 14 of the last 20 years and had her house arrest extended by a further 18 months in August for harbouring an American man who swam uninvited to her lakeside home.
But contact between the 64-year-old opposition leader and the military leadership has been stepped up in recent weeks, along with growing US moves to engage the generals after Washington recognised that sanctions and isolation were not bringing about the desired effect.
"She wrote that she wanted to co-operate for the benefit of the nation and asked to be allowed to explain some facts to the senior general"
Aung San Suu Kyi met a government minister in October and was later allowed to meet Kurt Campbell, the US assistant secretary of state who is the highest-ranking US diplomat to visit the country in 14 years.
In September she made a formal offer to the military government to help negotiate with Western countries to lift sanctions, which critics say have been largely ineffective.
The last meeting between Aung San Suu Kyi and Than Shwe was in 2002 in Yangon.
A number of websites run by exiled Myanmar activists carried a purported copy of the Burmese-language letter, which was addressed to the military chief.
The copy of the letter carried on the websites said: "I specially request a meeting with the Senior General to make a submission regarding co-operation with the State Peace and Development Council [the military government] for the benefit of the nation."
Nyan Win said he could not confirm the authenticity of the letter on the internet but added the full text of the letter would be released on Tuesday.
Myanmar's military, which has ruled the country for almost 50 years and is shunned by the West over its rights record, plans to hold multi-party elections in 2010.
But Aung San Suu Kyi's continued detention in effect rules her out from contesting and critics have denounced the proposed polls as a sham to further cement the military's hold on power.