According to other media reports, Branstad accepted the offer but refused to confirm it to journalists.
Trump had indicated prior to the November 8 election that he would consider Branstad for the job, given Iowa's successful business relationship with China.
Xi struck a friendship with Branstad during the first visit to Iowa in 1985, back when he was a low-level Chinese official, and the US governor helped arrange the second visit in 2012.
According to the US-China Business Council, in 2015 China was Iowa's second biggest export market after Canada. The US state is mainly exporting crops, machinery, beverages, tobacco, chemicals and electronics as well as services including travel, royalties and equipment maintenance.
Iowa exported $1.4 billion worth of crops to China in 2015, while the overall China exports profit totaled $2.3 billion.
