The report quoted "people with knowledge of the matter" and said a formal announcement could be made as soon as Friday.
The decision, which was not immediately confirmed by the companies, came a day after the Federal Communications Commission referred the proposed deal to a hearing in front of a judge -- a move that had been viewed as a "death sentence" for the plan because of the time and effort it would have taken.
The U.S. Department of Justice was also reported to be leaning towards blocking the merger on antitrust grounds should it have received FCC clearance.
Announced in February 2014, the $45 billion merger would have created a giant in the U.S. telecommunications space.
Together, the two companies account for a third of the U.S. pay TV market and about 40 percent of the wired broadband Internet market.
Martyn Williams covers mobile telecoms, Silicon Valley and general technology breaking news for The IDG News Service. Follow Martyn on Twitter at @martyn_williams. Martyn's e-mail address is martyn_williams@idg.com