A formal announcement could come as early as Friday.
Recent reports have circulated that the Justice Department would be presenting a case against the deal, joining the Federal Communications Commission against approval. Public interest groups have said the merger would not be a benefit for consumers.
A merged deal among the companies would give the combined entity up to 60% share of the U.S. broadband business and 30% share of U.S. cable TV-video distribution business.
Bloomberg said FCC officials told the two biggest U.S. cable companies on Wednesday they are leaning toward concluding that the merger does not help consumers.
Comcast believed the combine companies could mean big benefits for consumers when it comes broadband and video services.
News of the deal being dropped helped lift the stock prices of the companies during the day. Comcast closed 1.0% higher to $59.36, and the stock was up around 2.5% in midday trading. Time Warner Cable closed down 0.8% to $148.45. The stock had been 4% higher in midday trading.