"The senior general will meet Jim Webb tomorrow," one local official said on condition of anonymity, referring to Than Shwe.
He said Webb was scheduled to travel to Yangon, the commercial hub of Myanmar, on Saturday.
Webb, who is close to President Barack Obama, called in March for direct talks between the US and Myanmar.
But last month, he said the trial of Aung San Suu Kyi, the country's detained opposition leader, made it difficult for Washington to pursue "meaningful relations" with Myanmar.
The visit follows the conviction earlier this week of Suu Kyi and her sentencing 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, was sentenced to seven years of hard labour and imprisonment.
The convictions have been widely criticised around the world, particularly by the US government, and are likely to be raised by Webb in his talks with Myanmar officials.
The White House supported Webb's trip, saying his visit to Myanmar would convey "strong" US views of good governance to the country's leaders.
"We welcome Senator Webb's trip to the region, including the stop in Burma," Mike Hammer, a spokesman for the National Security Council, said, using the country's previous name.
"It is important for the Burmese leadership to hear of the strong views of American political leaders about the path it should take toward democracy, good governance, and genuine national reconciliation."
Larry Jagan, a Southeast Asia analyst, told Al Jazeera that "there is a danger in reading too much into this visit".
"We can't say there's going be a major shift in policy for the Obama administration and the Myanmar government," he said.
|Webb is expected to hold talks with senior General Than Shwe in Naypyidaw [AP]
"But this visit is extremely important because not even the UN envoy to Myanmar [Ibrahim Gambari] gets to see Than Shwe."
Webb is chairman of the US senate's Foreign Relations Committee's East Asia and Pacific Affairs Subcommittee.
Asked about speculation that Yettaw might be handed over to Webb, a spokesman for the US embassy in Yangon told the Associated Press said that the issue had "not been officially discussed".
However, Yettaw's lawyer, Khin Maung Oo, said he considered it unlikely.
"It is impossible that Mr Yettaw will be sent back with the visiting senator," Khin Maung Oo said.
"I think my client will finally be deported but not immediately."