Baucus, who has been a senator since 1978 and is chairman of the Finance Committee, announced this year he would not seek re-election next year.
Sen. Orrin Hatch, R-Utah, as well as several Senate aides and Baucus confidants confirmed Obama's decision to the Washington Post, though the White House and Baucus declined to comment.
"He ought to be confirmed immediately," Hatch, the ranking Republican on the Finance Committee, said, indicating the nomination wouldn't face much resistance.
Kenneth Lieberthal, President Clinton's national security director for Asia, told the newspaper Baucus understands international trade and said Obama was probably looking for "someone of stature, someone Chinese know has access to White House and understands politics at home."
"It's important to nominate and extend a prominent figure like him," Michael Green, a former Asia adviser in the George W. Bush administration, said.
The current ambassador, Gary Locke, announced last month he was resigning to rejoin his family in Seattle.
Locke has held the post since August 2011. Previously he was U.S. Commerce secretary and also served as governor of Washington.