Reuters/ Ueslei Marcelino
The role could be director of the Office of Management and Budget, according to the report. That office handles the government's budget policy.
Trump on Tuesday met with Cohn, who is the No. 2 executive at Goldman Sachs behind CEO Lloyd Blankfein.
The president-elect on Wednesday nominated former Goldman Sachs banker Steven Mnuchin as Treasury secretary. JPMorgan CEO Jamie Dimon had also reportedly been in the running for that role.
Steve Bannon, Trump's incoming chief strategist, is also a Goldman Sachs alum.
Trump was highly critical of Goldman Sachs and other Wall Street banks throughout his campaign.
He condemned Democratic nominee Hillary Clinton for her ties to the investment bank and other Wall Street firms - and for earning hundreds of thousands of dollars for speeches given to the bank and its clients.
Trump said in October that Clinton "meets in secret with international banks to plot the destruction of US sovereignty in order to enrich these global financial powers, her special interest friends and her donors."
To that, Goldman CEO Blankfein said in an October CNBC interview that "if there's some secret international cabal, I've been left out of the party."