"It's not easy to take a company that's losing money private", Galloway said.
"I don't have a controlling vote now & wouldn't expect any shareholder to have one if we go private", Musk said in a follow-up tweet.
Tesla now has a market value around $60 billion, which would make its take-private price tag about $80 billion, Galloway said.
Galloway said Musk likely wants to take the company private because he's anticipating third- and fourth-quarter losses, and is exhausted of dealing with irate investors and the general demands of being a public company.
At a share price of $420, Electrek points out that taking Tesla private would be a costly decision, to the tune of some $70 billion.
Tesla also made the news just before this tweet, when the Financial Times reported that Saudi Arabia's Public Investment Fund had amassed a previously unreported stake of "between 3 and 5 percent" of Tesla's shares.
Tesla did not immediately respond to a request for clarification.
In his tweet, Mr Musk said he could buy outstanding shares in the firm for $420 each, around a fifth higher than the share's current price.
"Funding secured", Musk said on Twitter. Musk has had feuds with regulators, critics and reporters, and questions remain about Tesla's production and manufacturing difficulties, long-term demand for its cars and uncertainty over funding. So it will take some very deep pockets to buy up all of Tesla's publicly held stock. Shares are up as high as 9% on the day.
George Galliers of Evercore ISI said he believed the tweet was serious.