Top Trump adviser and former Goldman Sachs executive Gary Cohn reportedly wants to lead the Federal Reserve

Gary Cohn, the former Goldman Sachs chief operating officer and current 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 and told friends that instead of the chief of staff job he would like to be named the chairman of the Federal Reserve.

Current Fed chair Janet Yellen's term expires in February 2018.

During the campaign, Trump attacked Yellen and accused her 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.

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

If Cohn were appointed Fed chairman, 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.

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