Rupert Murdoch (L) leaves the News Corporation building with his son Lachlan Murdoch (R) on July 21, 2016 in New York City.

Comcast said on Monday it had abandoned its bid for most of the assets of Rupert Murdoch's Twenty-First Century Fox, leaving Walt Disney as the sole suitor in pursuit of the $40 billion-plus deal.

Sources told Reuters last week that Disney was in the lead to acquire the assets, which include Fox's FX and National Geographic cable channels, its movie studio, the Star network in India and stake in European pay-TV provider Sky.

The Murdoch family, which controls Fox, prefers a deal with Disney because it would rather be paid in Disney stock than Comcast stock, and expects a potential deal with Disney to be cleared by U.S. antitrust regulators more easily, one of the sources said.

Comcast, the biggest cable provider in the United States, said in a statement on Monday that its discussions with Fox had ended.

"When a set of assets like Fox's becomes available, it is our responsibility to evaluate if there is a strategic fit that could benefit our company and our shareholders," Comcast said. "That is what we tried to do and we are no longer engaged in the review of those assets. We never got the level of engagement needed to make a definitive offer."

The assets in question would have expanded Comcast's international footprint through ownership of Sky and Star. A source told Reuters in mid-November that Comcast had approached Fox about its interest, and talks were in early stages.

Disney's negotiations with Fox are continuing, and a deal could be reached as early as this month, sources close to the situation said on Monday. The persons asked not to be identified because the deliberations are confidential.

Disney did not immediately respond to request for comment. A Fox representative declined to comment.

Any potential deal will follow the U.S. Department of Justice's decision last month to sue to block AT&T's $85.4 billion deal to buy Time Warner.

Comcast shares were up 1.5 percent in after-hours trading, while Disney shares were up 0.2 percent and Fox shares fell 1.3 percent.

(Disclosure: Comcast is parent of NBCUniversal and CNBC.)