But the UN chief said that because Aung Suu Kyi was on trial, Than Shwe told him he did not want to be seen as interfering with the judicial process, which the military ruler oversees, or being pressured by the outside world, the Associated Press news agency reported.
Ban, who was on a two-day visit to promote democratic reform in Myanmar, met Than Shwe twice in a plea to hold talks with the detained Nobel Peace laureate.
He also presented Than Shwe with a number of proposals to help the development of democracy.
He said those proposals included the release of the more than 2,000 political prisoners ahead of next year's election, opening of real dialogue between the government and opposition, and creating conditions conducive to free and fair elections.
It was not immediately known if Than Shwe agreed to the proposals put forward by Ban.
Ban himself had described his second visit to Myanmar as a "very tough mission" and made clear he was not expecting radical changes overnight in a country that has been ruled by the junta for 47 years.
"It is a setback for the international community and it is a missed opportunity for the Myanmar authorities," Ban said after his request to meet Aung San Suu Kyi was turned down.
Aung San Suu Kyi, who has spearheaded the campaign for democracy for two decades in the former Burma, is currently on trial for breaching terms of her house arrest by allowing an American intruder to stay at her home on May 4.
Critics have dismissed her hearing as a show trial and an attempt by the generals to keep her out of multi-party elections to be held next year.
Aung San Suu Kyi appeared in court on Friday but the trial was adjourned for a week because the judges had not received an earlier judgment barring two defence witnesses, her National League for Democracy said.