Washington (CNN) President Donald Trump told people Monday that he has settled on Larry Kudlow to replace Gary Cohn as the new director of the White House's National Economic Council, according to a source familiar with his conversations.

The President is known to change his mind at the last minute, and decisions are rarely final until they have been formally announced, but this is his latest thinking on Cohn's replacement.

Trump has spoken to Kudlow multiple times over the past week, a separate person familiar with the matter said, but Kudlow hasn't been formally offered the job yet and hasn't decided whether he would accept it.

The White House did not respond to a request for comment. Kudlow also declined to comment.

Kudlow's selection would be especially noteworthy because he is an avid free-trader who is firmly opposed to the sweeping tariffs on steel and aluminum imports that the President signed last week -- against the advice of Republican leaders on Capitol Hill and some of his own advisers. Trump suggested last Thursday that he wouldn't replace Cohn with someone who is similarly opposed to tariffs, which were one of the principal reasons that Cohn resigned.

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