Musk sent investors into a frenzy on Tuesday after tweeting that he was considering taking Tesla private at $420. "Funding secured," he wrote.
While Farley said the word "secured" may mean Musk has some people who are interested, he takes issue with a later tweet that says, "Only reason why this is not certain is that it's contingent on a shareholder vote."
"He's saying the funding is not only secured, it's certain," Farley said. "That's a bit outlandish."
"As a former regulator, the first thing I would have done is said 'Geez, are they running afoul of any rules here?' And I'm certain SEC is asking the same question," he added.
Farley said if he was still the head of the NYSE and Tesla was listed on his exchange, "I would have picked up the phone to our head of regulatory … and said, 'Hey this looks odd to me, I just want to make sure you are aware of it.' Immediately. I would have done that immediately."
Trading in Tesla shares was halted on Tuesday after the tweets.
Farley said the Nasdaq likely called Tesla to tell the company to release more information. Once that happened, there was a "smooth, steady" reopening of the stock, he pointed out.
However, "that should have happened before this tweet in the middle of the day," he said. "There are retail investors here that you have to worry about."
According to Dow Jones, the Securities and Exchange Commission has made inquiries to Tesla over the tweets.
Musk has provided no details on the source of the funding. At $420 a share, a full buyout would cost about $72 billion. However, Musk owns 22 percent of the company and he has suggested he would allow existing shareholders to maintain ownership, which would lower the cost.
Tesla has twice declined to comment on where the funding is coming from and did not immediately return a request for comment on Farley's remarks.
Tesla, which closed 11 percent higher on Tuesday, ended Wednesday down more than 2 percent.
— CNBC's Alex Sherman contributed to this report.