Gary Cohn. Kevin Lamarque/Reuters

Gary Cohn, the former Goldman Sachs chief operating officer who is now the top economic adviser to President Donald Trump, reportedly has his eyes set on the top job at the Federal Reserve.

According to Mike Allen of the news website Axios, a shake-up of the White House staff has put Cohn in contention to replace Reince Priebus as chief of staff. Such a move had long been rumored to come, but Allen added that a late surge in support among confidants of Trump could lead GOP lobbyist David Urban to get the job.

Cohn, according to Allen, wouldn't worry too much about being passed over for chief of staff and told friends he would rather be named Federal Reserve chair.

Fed Chair Janet Yellen's term expires in February 2018.

During his presidential campaign, Trump, without citing evidence, accused Yellen of collaborating with President Barack Obama and Democrats to keep interest rates low to ensure a victory for his competitor Hillary Clinton. His personal attacks led to speculation that he could even fire Yellen if he won.

After the election, however, Trump appeared to soften his stance on Yellen. During an interview in April, the president even suggested that he might reappoint Yellen after her term expired.

Cohn is the chair of the National Economic Council, but he has reportedly become one of Trump's most trusted advisers, particularly on economic subjects.

If Cohn were appointed Fed chair, it would add another person with Goldman Sachs ties to the Federal Reserve's key positions. Cohn was the second-in-command at the bank before leaving to join the Trump administration.

The New York Fed's president, William Dudley, was the bank's chief economist; the Minnesota Fed's president, Neel Kashkari, previously worked at Goldman; Patrick Harker, the head of the Philadelphia Fed, is a former trustee of the Goldman Sachs Trust; and Robert Kaplan, the president of the Dallas Fed, was vice chairman at Goldman in charge of investment-banking operations.