Aung San Suu Kyi, whose party won a massive victory in Myanmar's landmark elections last month, has met President Thein Sein to discuss the handover.
She also met army chief Min Aung Hlaing in the capital Nay Pyi Taw.
Both men have pledged to assist in a smooth transfer of power putting an end to decades of military-backed rule.
However, Ms Suu Kyi is constitutionally barred from becoming president and the army retains a quarter of seats in the upper and lower houses of parliament.
The constitution of Myanmar (also known as Burma) bars anyone whose children are foreign nationals from becoming president - Ms Suu Kyi's sons have British passports. However, she has repeatedly said that she will be above the person she nominates for the role.
The meetings each took about 45 minutes.
A spokesman for Thein Sein said his discussion with Ms Suu Kyi focused on how to achieve a peaceful transition of power.
Ye Htut told the BBC's Jonah Fisher that she did not broach the subject of changing the constitution to allow her to become president, nor was there any discussion around who the next president might be.
Her National League for Democracy (NLD) won about 80% of the seats up for election in the 8 November poll.
Despite hundreds of thousands of people, such as the stateless Muslim Rohingya minority, being denied voting rights, the elections were the most democratic in Myanmar in 25 years.
Ms Suu Kyi called on the president, parliament Speaker and army chief to meet her for talks after the elections - but full details of the talks are not expected to be released for some time.
The current parliamentary session ends in January. After that the new NLD-dominated parliament session, where they will choose a new Speaker before selecting two vice-presidents and a president, will begin.
The NLD secured the necessary two-thirds of the seats to control both houses of parliament, enabling it to choose the next president. But the army's quota of a quarter of the seats in both the upper and lower houses allows it to veto constitutional change.
It also controls key security ministries.
The army ruled Myanmar from 1962 until 2011, when a military-backed civilian government came into power led by Thein Sein and ushered in a series of reforms.