Larry Kudlow is the leading contender to head President Donald Trump's National Economic Council and would take the job if offered it, CNBC's Jim Cramer reported Monday.

Trump has not formally offered the job, but Kudlow is a leading choice of not only Trump but also some of his advisors to replace Gary Cohn as the president's top economic advisor. A White House official, who declined to be named, confirmed to CNBC that Kudlow is on the list of candidates but said the administration did not have personnel announcements to make.

Kudlow declined to comment.

Kudlow, a CNBC senior contributor and longtime on-air personality, helped to craft economic policy during the Reagan administration. Cramer worked with Kudlow on the CNBC show "Kudlow and Cramer."

Cohn announced his resignation as head of the National Economic Council last week after he lost his battle to block the Trump administration's move to levy tariffs on steel and aluminum. Kudlow advocates for free trade and generally opposes tariffs. He expressed his disappointment with Cohn's departure.

Kudlow informally advised Trump on taxes and other issues during his 2016 run for the presidency.

Market watchers had a negative reaction to Cohn's exit, as they worried about potential drawbacks frmo the tariffs. Critics are concerned that the trade actions could raise prices for consumers or lead to retaliation from trading partners that could hurt American companies.

Cohn's departure was seen as opening up a larger role for Peter Navarro, a trade hawk who has often supported a protectionist policy. Navarro has championed aggressive policy to combat what he deems trade abuses by China.

Over the weekend, reports surfaced that Trump had narrowed his search to two candidates: Chris Liddell and Shahira Knight. Liddell is the White House's director of strategic initiatives, and Knight is a National Economic Council deputy. Reports said Knight is not interested in the position.

— CNBC's Eamon Javers contributed to this report