The real-estate company controlled by Jared Kushner, President-elect Donald Trump’s son-in-law, has hundreds of millions of dollars in loans outstanding from domestic and foreign financial institutions, markets condominiums to wealthy U.S. and foreign buyers and has obtained development financing through a controversial U.S. program that sells green cards.

Those and other business activities could raise conflict-of-interest issues if Mr. Kushner is named to a staff position in the Trump administration. Executive branch employees...