The former president's planned talk with Musk comes on the heels of Democratic presidential nominee and Vice President Kamala Harris selecting Minnesota Gov. Tim Walz as her running mate. It also follows the disclosure of probes of a Trump-supporting political action committee that Musk says he created.

"ON MONDAY NIGHT I'LL BE DOING A MAJOR INTERVIEW WITH ELON MUSK — Details to follow!" Trump wrote in a post on Truth Social.

CNBC has requested comment from Musk.

On Monday, the North Carolina Board of Elections told CNBC it had opened an investigation of the America PAC political action committee, which Musk has said he created, after receiving a complaint that the group was collecting personal data from website users and failing to help users register to vote as promised.

The practices of America PAC, which is supporting Trump's candidacy, are also being eyed by the North Carolina Attorney General's Office and Michigan's secretary of state.

Musk is also the owner of the social media company X, which was previously known as Twitter when the company was publicly owned. Trump was for years an avid Twitter user before the site banned his account because he incited the Jan. 6, 2021, riot at the U.S. Capitol by a mob of his supporters.

The ban was lifted after Musk purchased Twitter for $44 billion.

Despite that, Trump uses Truth Social for his social media messages. The company is owned by Trump Media, a publicly traded company whose majority shareholder is the former president.