President Trump is strongly considering Christopher P. Liddell, a White House official who was an executive at Microsoft and General Motors, to succeed his departing top economic adviser, Gary D. Cohn, according to two people briefed on the discussions.

Mr. Trump has not made a firm decision, those briefed on the process said. But Mr. Liddell, the White House’s director of strategic initiatives, is currently seen as a front-runner to replace Mr. Cohn as the director of the National Economic Council, they said.

A White House spokeswoman did not respond to a request for comment.

Mr. Cohn announced his resignation this past week after losing a battle over the president’s longstanding desire to impose large tariffs on steel and aluminum imports.

The president has always wanted a prominent business figure to oversee the council, according to people who have spoken with him. But his aides, mindful of the difficulties they have had attracting people from outside the White House, have been looking internally, and a successor could be named as early as next week.