The country's democracy figurehead is currently banned from becoming president under the junta-era constitution.
Suu Kyi has held several rounds of closed-door talks with the powerful military since her National League for Democracy (NLD) party won crushing victory at elections in November.
Observers say the talks were likely aimed at testing the military's appetite for a constitutional change to allow Suu Kyi to the top job, a post many of Myanmar's people see as her destiny.
"We are going to hold the meetings... For MPs to be able to elect the president and vice presidents on March 10, Thursday, a week earlier than was previously announced," Win Khaing Than, speaker of Myanmar's combined houses of parliament, told lawmakers today.
More From This Section
The handover from a half century of military rule to a popularly elected government has been complex and drawn out -- and the army will continue to play a major role.
The main figures at the talks have in public tip-toed around the leadership issue. In typically cryptic comments on Tuesday, NLD spokesman Win Htein said the party stood behind an eventual Suu Kyi presidency.
"Aung San Suu Kyi must become the president... It just depends on whether it is earlier or later," he told reporters in the capital Naypyidaw.
Clause 59 (f) of the current constitution bars those with foreign children or spouses from the top office. Suu Kyi's late husband was British, as are her two sons.
Experts have so far been surprised by the relatively smooth passing of power from the military to a party led by its one-time nemesis Suu Kyi.
But the army retains sweeping political and economic powers. It is allocated a quarter of all parliamentary seats and will choose one of three candidates for president.