Lloyd Blankfein is preparing to exit the firm as soon as year end.
The company did not immediately respond to Reuters' request for comment.
Blankfein, 63, is planning to leave Goldman around the investment bank's 150th birthday in 2019, the Journal reported. Shares were mostly unchanged from their prices prior to the news.More news: As the Samsung Galaxy S9 Plus photographs in hard conditions
Blankfein is one of the longest-tenured Wall Street chiefs, exceeded only JPMorgan Chase boss Jamie Dimon, who recently revealed plans to stay on for another five years.
Solomon is an investment banker and advisor with an impressive track record who's worked directly with some of Goldman Sachs' most important clients.
Following the 2008 crisis, Blankfein became the poster child for Wall Street's role in fueling the meltdown. In 1982, he quit his job as a tax lawyer and joined Goldman's commodities arm as a gold salesman. Even before the report, Goldman's shares were higher, bouncing after the Friday jobs report suggested that the US economy remains healthy but not enough to force the Federal Reserve to act aggressively to tamp down rising prices or inflation.