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.
A spokesman for the US embassy in Yangon told the Associated Press that Webb was expected to spend three days in Myanmar and would visit the new administrative capital of Naypyidaw to meet government leaders.
The spokesman however gave no details as to who the senator would meet.
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, the embassy spokesman 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."