India-born Parag Agrawal, who was appointed as Twitter's CEO in November last year, is expected to stay on until the firm is sold to Musk, the report said.
According to Reuters, the Tesla CEO has lined up a new CEO for Twitter.
Readying the war chest
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"Great to connect with you my "new" friend @elonmusk ... Kingdom Holding Company and I look forward to roll our ~$1.9 bn in the "new" Twitter," Alwaleed said in a tweet.
Legal troubles
Meanwhile, the US Federal Trade Commission (FTC) is reviewing Musk's $44 billion takeover of Twitter, Bloomberg reported on Thursday, citing a person familiar with the deal.
Musk must notify the FTC and the Justice Department of the purchase and wait at least 30 days before closing to allow for an examination into potential antitrust problems, according to US merger laws. The FTC is also looking into whether Musk should have notified the authorities when he bought a 9% stake in the firm in March.