The race to replace Gary Cohn as Trump's top economic adviser is heating up - and 2 big names have become the frontrunners

Kevin Lamarque/Reuters

Gary Cohn and President Donald Trump

• Rumors are already flying about who will replace Gary Cohn as President Donald Trump's top economic adviser.
• CNBC's Jim Cramer reported on Monday that Larry Kudlow, with whom Cramer hosted a show from 2002 to 2005, is the front-runner.
• The New York Times reported Saturday that Christopher Liddell, a former Microsoft and General Motors executive currently working in the White House, is the frontrunner.
• Trump's pick will be a major sign about his economic agenda going forward.

The race to replace Gary Cohn as the National Economic Council director and as President Donald Trump's top economic adviser is heating up.

Almost as soon as Cohn announced his resignation on Tuesday, speculation over his replacement - and the direction of Trump's economic policy - kicked off. Now, according to two reports and sources, two clear frontrunners have emerged.

According to CNBC's Jim Cramer, fellow CNBC personality Larry Kudlow is the leading candidate. Kudlow, who cohosted a CNBC show with Cramer from 2002 to 2005, was previously floated for other economic jobs in the Trump administration.

Separately, a source who has advised Trump on economic issues told Business Insider last week that Kudlow was a leading candidate for the job.

Kudlow served as a staff economist during the Ronald Reagan administration, was chief economist for Bear Stearns from 1987 to 1994, and has regularly appeared on CNBC since 2001.

The New York Times' Maggie Haberman and Jim Tankersley reported Saturday that former Microsoft executive Christopher Liddell was considered the leading candidate for the job. Liddell is currently the White House's director of strategic initiatives and was previously CFO of Microsoft and General Motors.

Investors and economists are watching the pick closely since it could indicate the direction of Trump's economic agenda - particularly, now, with respect to trade. A choice favoring trade barriers could set off concern that Trump will lean into his protectionist tendencies. Cohn was seen as a free-trade advocate who pushed back on Trump's desires for large tariffs and trade restrictions.

Kudlow has been critical of Trump's approach on trade and recently blasted the president's decision to impose broad tariffs on imports of steel and aluminum. His selection would fill a void of pro-free-trade advocates that developed in the White House over the past few months.

Liddell's economic views are less clear. According to the Times, however, he told a New Zealand newspaper after Trump's election that "the days of unbridled free trade and unbridled free markets are over."