Sources familiar with the matter told the outlet that the deal would involve TikTok's U.S. operations.
TikTok and Twitter declined to comment.
Twitter would be the latest bidder for the popular video-sharing mobile app. Currently, Microsoft remains TikTok's highest bidder and announced in a blog post earlier this month that it would continue discussions for a potential purchase of the company.
"Microsoft fully appreciates the importance of addressing the President’s concerns," the company said. "It is committed to acquiring TikTok subject to a complete security review and providing proper economic benefits to the United States, including the United States Treasury."
TikTok, owned by Chinese firm ByteDance, has been deemed a national security threat by the Trump administration, which argues the company could potentially share users' data with the Chinese government.
President Trump signed an executive order on Thursday that will ban Tiktok on Sept. 15 unless the company finds a buyer for its U.S. operations.
China has firmly opposed the executive order, with ministry spokesman Wang Wenbin telling reporters on Friday that the U.S. is "using national security as an excuse and using state power to oppress non-American businesses." Wang added that the move by the U.S. is political, noting that it “will only lose its moral high ground with a damaged image and a deficit of trust.”
Meanwhile, Tiktok has threatened to take legal action against the Trump administration.
"We are shocked by the recent executive order, which was issued without any due process," TikTok said in a statement. "For nearly a year, we have sought to engage with the U.S. government in good faith to provide a constructive solution to the concerns that have been expressed."
The company argues the administration "dictated terms of an agreement without going through standard legal processes and tried to insert itself into negotiations between private businesses."
While it is not immediately clear how much TikTok's valuation would be, Twitter does not have nearly as much financial power as its competitors. The company reported a loss of $1.2 billion in revenue for the second quarter with about $7.8 billion in cash and short-term investments as of June. In comparison, Microsoft has roughly $136 billion in cash. Twitter's market cap is more than $29 billion; Microsoft's market cap is about $1.6 trillion.
Sources have told FOX Business' Charlie Gasparino that Microsoft has sought outside partners to help finance the massive transaction, which could be valued anywhere from roughly $20 billion to $100 billion.
Twitter argues that due to its size it would face less antitrust scrutiny than larger bidders, like Microsoft, people familiar with the discussions told the Journal.
TikTok has 800 million users worldwide and 100 million in America alone.