Blankfein has worked for Goldman Sachs since 1982, after spending four years in law practice.
The 63-year-old will be leaving on his own terms, The Wall Street Journal reported.
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. Visit MarketWatch.com for more information on this news. He's preached patience to investors while pointing to strong results in the firm's other businesses, including investment banking.More news: Fortnite: Battle Royale is heading to iOS and Android
Cohn resigned his position at the White House earlier this week and is not expected to return to Goldman.
"The departure would conclude a 36-year Goldman career for Mr. Blankfein, the son of a Brooklyn postal worker who rose to the pinnacle of Wall Street". He initially joined Goldman's commodities trading arm, and after 12 years, he was promoted to co-head of the currency and commodities division.
Blanknfein, the longest serving CEO at Goldman, succeeded Henry Paulson in 2006, who left to serve as Secretary of the Treasury. He was considered at the time as the most likely successor to Blankfein. Even though he supported Hillary Clinton during the 2016 election, Blankfein recently told CNN the economy is "higher" under Trump than if Clinton had won. In recent years, the firm has been hit by a slowdown in the markets business, as 2017 was its worst year in trading under Blankfein's watch.
Nowhere was the news met with more surprise than inside Goldman Sachs.