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