Terry Branstad was seen entering Trump Tower in New York on December 6 for talks with the president-elect.
He called Xi Jinping a “long-time friend” when the he visited Iowa before becoming Chinese president.
After Bloomberg first reported the nomination, which requires Senate confirmation, Beijing responded by calling Terry Branstad an “old friend”.
China’s Foreign Ministry spokesman Lu Kang said: “We welcome him to play a greater role in advancing the development of China-US relations.”
However, Terry Branstad’s spokesman said reports of the nomination were “premature”.
Donald Trump has also reportedly tapped General John Kelly to run the Department of Homeland Security.
John Kelly would be the third general Donald Trump has selected for a high-level position in his administration.
Terry Branstad’s appointment is seen as key at a time of trade tensions between the world’s two biggest economies.
Donald Trump has accused China of “raping” the US by devaluing its currency and giving itself an unfair exporting advantage.
There has also been a political row over a phone call between Taiwan’s leader and Donald Trump.
The call broke decades of US diplomatic protocol and prompted a protest from China.
Although the Trump team said it was spontaneous, there is growing evidence that it was planned weeks in advance.
Most recently, the New York Times reports that former Senator Bob Dole worked behind the scenes to engineer the communication.
Terry Branstad said in a statement after December 6meeting that he had enjoyed a “very cordial conversation” with Donald Trump.
His spokesman said reports of his nomination were “premature and not accurate”.
President Barack Obama has been helping Donald Trump with his appointments, the Republican businessman said on December 7.
One of Barack Obama’s recommendations had been followed, said Donald Trump, without naming which job it was.
In an interview after he was named Time Magazine Person of the Year, Donald Trump also confirmed a report that he had sold all his stocks in June.
Without any tax returns disclosed, there is no evidence to support his assertion, or to assess the value of the sale.
Donald Trump has promised to make an announcement next week on how he intends to step away from his multi-billion-dollar business empire.
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