Clayton, who is known for working on top IPOs such as the Alibaba Group's, met Trump on 22 December, according to Reuters.
He has moved ahead of Debra Wong Yang, a former U.S. Attorney under President George W. Bush. It was speculated in December that she was in line for the job.
As a partner at international law firm Sullivan & Cromwell, Clayton has expertise in both public and private mergers and public offerings. He has worked on Barclays Capital's acquisition of the Lehman Brother's assets during the financial crisis of 2008, the sale of Bear Stearns for JP Morgan and the U.S. Treasury's investment into Goldman Sachs.
Other contenders that have been floated for the role include former SEC boss Paul Atkins and lawyer Ralph Ferrara.
Many of the candidates have been interviewed for the job by Carl Icahn, an investor who took on a crucial role in the Trump team back in December.