Citing a company-wide email the network said it obtained, CNBC reported the space travel pioneer would be paying $70 a share -- 25 percent above the $56 a share the stock traded for in February after a stock split.
That would value the 20-year-old firm -- the first private company to send astronauts into orbit, among many other firsts -- at $127 billion.
That valuation has climbed steadily in recent years as SpaceX raised billions to finance work on its next-generation Starship rocket and its Starlink global satellite internet network.
Meanwhile, independent online website Insider reported this week that SpaceX had paid $250,000 to resolve a complaint for alleged sexual misconduct by Musk against an attendant on a SpaceX corporate jet.
The 50-year-old Musk has rejected the charge, saying Thursday on Twitter that "for the record, those wild accusations are utterly untrue."
Musk, who is also the CEO of carmaker Tesla, said he was making a $44 billion offer to buy Twitter.
But this week he said he first needed clarity on the prevalence of fake or spam accounts on the popular social media platform before moving forward with the purchase.
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