The announcement could be made as soon as Monday, the paper reported on Sunday citing sources, and will formally establish Solomon as the successor to Lloyd Blankfein.
Blankfein told CNBC earlier this year that he expected Solomon to succeed him when he decides to leave. The Wall Street Journal reported in March that Blankfein could step down as chief executive at the end of the year.
Blankfein, one of the longest-serving CEOs on Wall Street, will stay on for an interim period, the New York Times report said.
Goldman Sachs declined to comment.
Solomon, who joined the investment bank as a partner in 1999, is currently president and chief operating officer of the bank.
(Reporting by Shubham Kalia in Bengaluru; Editing by Gopakumar Warrier and Saumyadeb Chakrabarty)
