Thein Sein, who would be the first leader of the country to visit in half a century, is planning to be in the American capital around May 20 or May 21, a staff member at the US Congress told AFP on condition of anonymity.
The trip would include a summit with President Barack Obama at the White House. Administration officials declined immediate comment but have previously said that they were studying a visit by Thein Sein.
The source said the United States was considering as another gesture a change in US policy to call the nation Myanmar, the leaders' preferred usage, and not the previous name of Burma, which is used by exile groups.
The United States is also looking at whether to include Myanmar under the Generalized System of Preferences, through which the United States offers duty-free access for up to 5,000 products from developing countries that meet labor standards.
It would be the first visit to Washington by a head of the country since military leader Ne Win was invited in 1966 by president Lyndon Johnson.
Thein Sein has previously visited the United States to attend the UN General Assembly, but only held meetings in New York.
Thein Sein, a former general, surprised even many skeptics after taking office in 2011 as a nominal civilian by undertaking a range of reforms, including freeing political prisoners and relaxing censorship.
He has also allowed opposition icon Aung San Suu Kyi to take a seat in parliament, a once unthinkable gesture as the Nobel Peace laureate spent most of the previous two decades under house arrest.
Obama paid his own visit to Myanmar in November when he praised the nation for its transition but called for progress on reforms, particularly in the treatment of ethnic minorities.
But Thein Sein's visit is expected to be controversial due to a surge in violence against the Rohingya, a Muslim people who are not considered citizens by Myanmar.
A recent Human Rights Watch study accused Myanmar of a "campaign of ethnic cleansing" against the Rohingya, saying that at least 211 have been killed since June 2012 and tens of thousands more forcibly displaced.
Jennifer Quigley, executive director of the US Campaign for Burma, a Washington-based pressure group, accused the Obama administration of only responding to positive developments and not to setbacks.
"To invite him at this point of time would really just reinforce the message of a positive relationship when there really has been no move by the US government to tie this to the Burmese government taking necessary steps" to curb the violence, she said.
Quigley voiced concern about the anti-Rohingya use of force and also the situation in Kachin state, where tens of thousands have been displaced since a ceasefire between the government and ethnic rebels broke down in June 2011.
The United States has already eased key sanctions against Myanmar and has allowed US businesses to invest in the country, which has seen a surge of interest by investors since the launch of reforms.
The congressional source said that Obama may try to send a signal to Myanmar by renewing his authority to impose sanctions, which remain on the books but have been waived.
The European Union last week ended the last of the bloc's sanctions against Myanmar, with the exception of an arms embargo.
Even before the reforms, most Asian nations conducted business with Myanmar, which had developed a close relationship with neighboring China.
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