He had been co-head of the bank's trading division before being promoted to chief financial officer in 2013, while Solomon, 56, had been a co-head of investment banking at Goldman since 2006 until becoming co-COO.
The Journal, citing people familiar with the matter that it didn't identify, said Blankfein, 63, could leave this year and the bank meant to replace him with one of its two co-presidents, David Solomon or Harvey Schwartz.
"I look forward to continuing to work closely with David in building our franchise around the world, serving our expanding client base and delivering strong returns for our shareholders", said Blankfein.
The chief executive of Goldman Sachs has said reading a report forecasting his imminent retirement plans was like hearing his own eulogy - indicating the bank's boss is staying put for the near future.
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Solomon previously worked at Bear Stearns and Drexel Burnham Lambert - the investment bank that pioneered the use of junk bonds for corporate takeovers under Michael Milken, who was jailed for securities fraud. He has served a dozen years at the top of Wall Street's most powerful firm. Blankfein later tweeted that he hasn't made an announcement.
Schwartz has been co-president and chief operating officer since January 2017.
Solomon, 55, joined Goldman Sachs in 1999 as a partner, one of the most coveted roles on Wall Street and a clear sign of his seniority at the time.
The bank typically maps out its succession planning by naming two or three candidates to top roles.
If Solomon does inherit the CEO job from Blankfein, he may have his work cut out for him.