Dorsey wanted the decade-old social media business to not change course and remain focused on products that users are familiar with, the Bloomberg report said.
Williams wanted to explore selling Twitter, the article said, and explained that ultimately Dorsey lost the disagreement.
The board of directors decided to hire Goldman Sachs and Allen & Co. to evaluate possible bids.
With suitors like Disney, Salesforce and Google lining up to buy the Silicon Valley-based company, Twitter is now consulting with advisors to settle the internal conflict, people familiar with the situation told Bloomberg. Dorsey does not want to sell Twitter, even though Bloomberg points out that formal bids may or may not even come. However, according to the news service, Dorsey may be overruled by the board to make Twitter an independent company.
Sources told Bloomberg that Dorsey does not want to be the sole decision maker on Twitter's future. The article mentioned that Chief Financial Officer Anthony Noto has become just as influential as Dorsey, saying that it is not known if Noto supports the sale.
Noto, who was the former CFO of the NFL, bought the rights to stream 10 of the league's games. With Noto, Twitter has entered the video streaming realm, the report said.
CNBC has reached out to Twitter, Disney and Google for comment. Salesforce declined to comment.
Even with the gains from live video streaming, Bloomberg said Dorsey is still having to consider a different future for Twitter — weighing a sale because of the lack of user growth.
For more on the subject read Bloomberg's article here.