BEIJING — Iowa’s governor, Terry Branstad, hopes to be America’s next ambassador to China, and if he is confirmed as President-elect Donald J. Trump’s envoy in Beijing, his new home there may be just three hours’ drive from a transplanted patch of his home state.

Plans are afoot to build a “model farm” in northern China inspired by one in Iowa that Xi Jinping visited in early 2012, before he became China’s president. The idea has highlighted Mr. Xi’s peculiarly long relationship with the Midwestern state and with Mr. Branstad, who was Iowa’s governor from 1983 to 1999 and then returned to office in 2011.

The farm is still just a proposal, according to Chinese officials and Iowans involved in the discussions. But in a few years visitors to Chengde, in Hebei Province, may be able to stop at an Iowa-style farm, perhaps even including a replica of the home that Mr. Xi visited. And these days, anywhere that Mr. Xi visits has official pulling power in China.

“There is a strong desire, somewhat, to retrace President Xi’s footsteps and also to understand how we do things, because President Xi has held us up as an example,” Grant Kimberley, whose parents’ farm in Iowa hosted Mr. Xi and inspired the proposed model, said in a telephone interview. “I’m sure it’s a motivation for the project.”