"It's not easy to take a company that's losing money private", Galloway said.
The tweets came after a report in the Financial Times that Saudi Arabia's sovereign wealth fund had taken a 3%-5% stake in Tesla, a holding worth at least $1.9bn.
Tesla did not respond to a request for comment immediately.
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Typically, buyouts like this involve a new investor buying out smaller shareholders, since there are regulatory barriers to a privately held company having many small shareholders.
At US$420 per share, a deal would represent a 22.8 per cent premium to Tesla's closing price on Monday, making it one of the biggest go-private deals with a price tag of about US$72 billion. The figure even drew some jokes on Twitter about whether it was a pot reference, with 420 being a common slang term for marijuana.
"Funding secured", Musk said on Twitter.
He is also under intense pressure to prove he can deliver consistent production numbers for the Model 3 sedan, Tesla's lowest-priced model and the key to its plans to become a mass-market automaker, after a host of manufacturing challenges and concerns it was burning cash too quickly. Earlier this year, he caused a stir during a first quarter earnings call when he angrily cut off two analysts whose questions annoyed him.