Bloomberg, citing sources, reported that Branstad had agreed to take the position.
"We welcome him to play a greater role in advancing the development of China-U.S. relations," Foreign ministry spokesman Lu Kang told a daily press briefing when asked about the report Branstad would become ambassador, according to Reuters.
Lu did not confirm the Bloomberg report and said China would work with whoever became ambassador.
Branstad's office could not be immediately reached for comment on the report and Trump's office did not immediately respond to a request for comment by Reuters, outside business hours.
Trump had been scheduled to meet Branstad on Tuesday, his transition team said earlier, without elaborating.
Trump's dealings with China have been in focus since Taiwan President Tsai Ing-wen called him last week to congratulate him.
The call raised consternation in Beijing, which sees the self-ruled island as a renegade province and objects to other governments dealing with it.
Trump's conversation with Tsai was the first such contact with Taiwan by a U.S. president-elect or president since President Jimmy Carter adopted a "one-China" policy in 1979, recognizing only the Beijing government.
China suspects Tsai wants to push for the formal independence of Taiwan.
Branstad called Chinese President Xi Jinping a "long-time friend" when Xi visited Iowa in 2012.