Under the deal, Musk and Tesla would have had to pay a nominal fine, and the CEO would not have had to admit any guilt, the sources said. However, the settlement would have barred Musk as chairman for two years and would require Tesla to appoint two new independent directors, CNBC's David Faber, citing sources.
Musk refused to sign the deal because he felt that by settling he would not be truthful to himself, and he wouldn't have been able to live with the idea that he agreed to accept a settlement and any blemish associated with that, the sources said.
Tesla did not immediately reply to CNBC's request for comment about the collapse of the deal at the last minute, which was disclosed to Andrew Ross Sorkin by sources who spoke on condition of anonymity.
Musk said Thursday the SEC's allegations are "unjustified" and that he acted in the best interests of investors.
"Tesla and the board of directors are fully confident in Elon, his integrity, and his leadership of the company, which has resulted in the most successful U.S. auto company in over a century. Our focus remains on the continued ramp of Model 3 production and delivering for our customers, shareholders and employees," said Tesla's board of directors in a statement.
The SEC sued Tesla on Thursday, alleging fraud over Musk's tweet on Aug. 7 in which he announced he was planning to take the company private and had secured funding for the deal. It would have been the largest such transaction of its kind.
Musk later said in a blog post he had been approached by the Saudi Arabian sovereign wealth fund multiple times about investing in Tesla, making him confident he would be able to secure the funds needed to take the company private at his price of $420 per share.
Musk called off his plans to take Tesla private on Aug. 24.
The Wall Street Journal was first to report news of the proposed settlement Musk turned down.
For Tesla, the stakes are high. It is unclear if Musk will step down and what the company would be like without him at the helm. These issues have been a distraction for the company, which has been trying to ramp up production of its first mass market vehicle, the Model 3.
There is about a 25 percent chance Musk remains CEO of Tesla now that the SEC is suing the company, said Gene Munster, a managing partner of venture capital firm Loup Ventures, which invests in technology companies.
The settlement notably would have gone some way in eliminating some the overhang on the stock.
Since Musk so far has chosen to fight this, it could take years to reach an outcome, Bernstein analyst Toni Sacconaghi said in a note Friday.
"In the absence of a settlement, the mere possibility that Musk could be removed as CEO (or entirely from Telsa) is likely to cast an overhang on the stock, and make it extremely difficult for the company to raise capital (either private or public)," Sacconaghi said.
It is still possible Musk will settle with the SEC, said Charles Elson, director of the Weinberg Center for Corporate Governance at the University of Delaware.
"These things almost always settle," Elson said. "The consequences of not settling it are a lot worse, and this is a pretty straightforward case for the SEC."
The SEC could impose hefty fines and ban Musk from serving as an executive or director of a publicly traded company for life. The charges also open up Tesla to lawsuits from investors who bought and sold shares based on Musk's tweet about going private.
Shares of Tesla plummeted nearly 14 percent, marking the stock's worst day since Nov. 6, 2013. The stock is down about 30 percent from its 52-week high of $387.46, which it hit on the day of Musk's tweet.
Analysts have been revising their opinions on Tesla since the charges were reported. On Friday, both Citigroup and CFRA downgraded Tesla's stock to a sell, citing the SEC's suit. CFRA also cut its price target to $225 from $265.