Salesforce confirmed Benioff's comments to CNBC and declined to comment further. CNBC has reached out to Twitter for comment.
Twitter shares fell as much as 8 percent and ended the day down about 5 percent. Salesforce shares popped as much as 8 percent, but pared those gains to end the day 5 percent higher.
After reports that companies like Google and Disney had already backed off bids for Twitter, Salesforce had been left as the most likely suitor, the Financial Times reported. But Benioff came under pressure from shareholders, who questioned the match between the social media company and the enterprise technology firm, according to the FT.
"All I can do is one thing, which is wish my good friend [Twitter CEO] Jack Dorsey well," Benioff told CNBC last week. "He's the CEO of that company. It's his job to make that a great company, but it is my job to make Salesforce a great company."
Sources told the Financial Times the Twitter sales process is "virtually dead." Still, sources told CNBC as late as last week that there were other bidders beyond Salesforce interested in buying Twitter, which has struggled to monetize tepid user growth amid new live-streaming initiatives.
— Reporting by CNBC's David Faber and CNBC staff.