The opposition National League of Democracy had won about 70 percent of the votes counted by midday today, said party spokesman Win Htein.
The comments, if confirmed by official results, indicate that Suu Kyi's party would not only dominate the Parliament but could also secure the presidency despite handicaps built into the constitution.
"I want Mother Suu to win in this election," said Ma Khine, a street vendor, referring to the 70-year-old Suu Kyi with an affectionate term many here use. "She has the skill to lead the country. I respect her so much. I love her. She will change our country in a very good way."
The government election commission was expected to start announcing final results this evening. The NLD has been widely expected to finish with the largest number of seats in Parliament.
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No matter the results, the election will not create a fully democratic Myanmar, which ended a half-century of military rule in 2011, followed by a quasi-civilian government run by a party made up of former military figures now expected to fare badly in the elections.
The amendment bars anyone with a foreign spouse or child from holding the president's and vice presidents' positions. Suu Kyi's two sons are British, as was her late husband. Suu Kyi, however, has said she will act as the country's leader if the NLD wins the presidency, saying she will be "above the president."
In her first comments after yesterday's elections, Suu Kyi told a crowd gathered at the NLD party headquarters that while vote tabulations wouldn't be announced until later, "I think you all have the idea of the results."