Somebody needs to wake-up Trump from an economic agenda that's "off the deep end," something Kudlow would not be able to do, Stockman argued on CNBC's "Fast Money Halftime Report."
Kudlow is a "Wall Street cheerleader," added Stockman, who was Kudlow's old boss at the Office of Management and Budget during the Reagan administration.
Cohn, president of Goldman Sachs before joining team Trump, announced his resignation last week from his White House post after he lost his fight against steel and aluminum tariffs.
Kudlow, an unapologetic free-trade advocate throughout his career, has recently softened his stance on China as a bad actor. That would put in him in good standing with Trump's views, said Cramer, who worked for years on their onetime CNBC show, "Kudlow and Cramer."
But like Cohn, Kudlow has said recently on CNBC he would have advised the president not to pursue tariffs as a way to bring China and other unfair traders to heel. Kudlow was an informal advisor to Trump during the 2016 presidential campaign.
While much of the speculation surrounding a Kudlow pick was around trade on Monday, Stockman said any drag from trade policy is far outweighed by the looming Trump "fiscal disaster."
Kudlow thinks the U.S. economy can grow its way out of rising deficits, but this late in the business cycle post-Great Recession that's not possible, Stockman argued.
In his reporting, Cramer, host of CNBC's "Mad Money," stressed that no decision by Trump has been made on Kudlow or anyone else to take Cohn's place.