A Russian businessman who explored building a tower in Moscow with Donald Trump’s company during the presidential campaign is a little-known developer of working-class apartments on the city’s outskirts.

Andrei Rozov’s development background might seem an unlikely match for the opulent Trump Organization. But the businessman, whose name hasn’t previously been reported in regard to this project, had a connection to the president’s firm: He and Trump associate Felix Sater both worked for a Russian property tycoon named Sergei...