Jim Webb to discuss sentencing of Suu Kyi during meeting with General Than Shwe.
Webb, who arrived in Naypyidaw, the country's remote administrative capital, on Friday, is in Myanmar on the second leg of a two-week tour of the region.
Webb is travelling with a US delegation that would meet the Union of Myanmar Federation of Chambers of Commerce and Industry in Yangon, the commercial hub, a Myanmar businessman said on condition of anonymity.
Webb had called in March for direct talks between the US and Myanmar.
But last month, he said the recent trial of Aung San Suu Kyi, Myanmar's detained opposition leader, made it difficult for Washington to pursue "meaningful relations" with Myanmar.
His meeting was likely to include talks on Suu Kyi, who was sentenced earlier this week to another 18 months of house arrest.
A US national, John Yettaw, who triggered the trial when he swam to her lakeside home in Yangon in May, was sentenced to seven years of hard labour and imprisonment.
After his talks in Naypyidaw, Webb was due to fly to Yangon, where Suu Kyi and Yettaw are being held.
In a surprise development, Webb could meet Suu Kyi herself and Yettaw, according to local officials.
The White House said it supported Webb's trip, adding that his visit to Myanmar would convey "strong" US views of good governance to the country's leaders.