There was no immediate comment from the White House on the disclosure, which was made by officials who spoke on condition of anonymity.
Kathy Weber, a spokeswoman in Baucus' office, declined to confirm the move but said, "Max has given his life to public service and when asked to serve he takes that request very seriously."
Obama has been searching for a new top diplomat in Beijing as he executes a so-called Asia pivot in U.S. foreign policy to more directly counter China after the wars in Iraq and Afghanistan.
The relationship between the two nations has grown more troubled in recent weeks as Chinese authorities unilaterally declared an air defense zone over disputed islands in the East China Sea. The United States subsequently flew a pair of B-52 bombers through the space last month without incident. Vice President Joe Biden sought to calm matters on his recent trip through Asia.
Baucus, 72, was first elected to the Senate in 1978 and since early 2007 has been chairman of the Senate Finance Committee. On some key issues, he has pursued a more moderate approach than some fellow Democrats would prefer, a reminder that he hails from a rural, Western state.
The panel has jurisdiction over taxes, trade, health care and more. As committee chairman, Baucus has pressed both Democratic and Republican administrations to take a harder line against what he says are unfair Chinese trade practices. The country has the largest trade surplus of any nation with the U.S., and American manufacturers claim it is manipulating its currency to maintain that imbalance.