Donald Trump’s successful insurgent bid for the White House promised to upend a global power structure that benefited large corporations. Now, several Wall Street financiers and other successful business leaders could be in line to run top posts in his presidential administration.

People close to Mr. Trump have said he is considering Steven Mnuchin, a former Goldman Sachs Group Inc. banker who became his national campaign finance chairman in May, as his pick for Treasury secretary. If tapped for the job, Mr. Mnuchin would...