Suu Kyi was freed from house arrest in 2010 and holds a seat in Myanmar's Parliament, a position she secured in elections in 2012. She won the Nobel Peace Prize in 1991 for her pro-democracy campaign.
Myanmar President Thein Sein was recognized by the International Crisis Group this week for political reform efforts that coincided by Suu Kyi's release.
Htay Oo, vice chairman of the ruling Union Solidarity and Development Party, said there are no plans to make way for a Suu Kyi presidential bid.
"Our party has not considered yet to review the constitution," he told Thai newspaper The Irrawaddy.
Suu Kyi is prohibited from running for president because the law forbids candidates with foreign children. She has two children from her marriage to Michael Aris, a British national.
Win Tin, a member of her opposition National League for Democracy, said she'd face an uphill battle for the presidency even with a legal maneuver.
"Her rival groups in Parliament will try hard to prevent her from becoming president," he said.
The Thai newspaper reports a constitutional measure was suggested during the New York ceremony honoring Myanmar's president.