Htin Kyaw, a respected writer who helps run Suu Kyi's charitable foundation, was seen as the top choice to act as a proxy for the democracy veteran who is barred from the office by a junta-scripted charter.
One further vote of approval is needed in the combined houses dominated by Suu Kyi loyalists before Htin Kyaw can officially be anointed leader of the nation that has been run by the military for decades.
The decision is likely to prove controversial in a country still burdened by the legacy of nearly 50 years of rule by the military, which retains significant influence including a quarter of the parliament's seats.
Suu Kyi is beloved by many in Myanmar and the uncontested figurehead of the country's long democracy struggle, but months of negotiations have failed to convince the military to change a charter clause that blocks her from top office.
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The combined houses are expected to vote between three candidates next week, with a new president set to replace outgoing President Thein Sein at the end of March.
With the NLD dominating both houses, Htin Kyaw is likely clinch the top post with a comfortable lead.
The NLD's other candidate is from the upper house, ethnic Chin MP Henry Van Thio. Both he and Myint Swe would then become vice presidents.
Though he did not run in November's polls, Htin Kyaw is a close and trusted confidante.
He sometimes drove for the democracy activist during her brief moments of freedom from house arrest, and was at her side when she was finally freed in 2010.