Twenty-First Century Fox, the media empire run by Rupert Murdoch, made an $80bn (£47bn) takeover bid in recent weeks for Time Warner – whose stable includes Game of Thrones channel HBO.
According to the New York Times, the Murdoch company offered to buy Time Warner for $85 (£50) per share in a cash-and-stock bid, adding that Mr Murdoch was determined to buy the company and was unlikely to walk away.
Time Warner shares jumped more than 13% on Wednesday morning following the report. The company could not be immediately reached for comment.
As part of the proposal, Fox indicated that it would sell CNN to ward off potential anti-trust concerns since Fox News competes directly with CNN.
Putting CNN on sale would probably lead to a bidding war for the news channel as CBS and ABC, a unit of the Walt Disney, have long been seen as interested suitors, the newspaper said.
Fox first approached Time Warner in early June. Chase Carey, the president of Fox and a long-time top lieutenant to Mr Murdoch, met privately with Time Warner's chief executive officer, Jeff Bewkes, the newspaper said.
Later that month, Fox delivered a formal takeover proposal worth $85 in stock and cash for each Time Warner share.
Nathaniel Brown, a Fox spokesman in New York, declined to comment on the report.
The bold approach could be the beginning of another reshaping of the media industry, prompting a new spate of mega-mergers among America's entertainment giants.
Mr Murdoch has built his global media empire over decades partly by pursuing bold deals that were often rebuffed at first by the targets of his overtures, only to later acquiesce.
Together, Fox and Time Warner would become a colossus with an array of television networks and channels like Fox, Fox News, FX, TNT and TBS, the premium subscription channel HBO, movie studios like Twentieth Century Fox, Warner Brothers and other high-profile outlets.
HBO is about to start filming season five of the hit fantasy series Game of Thrones in Northern Ireland.
It would also combine Fox's growing sports business with the broadcast rights that Time Warner owns for professional and college basketball among other sports. The merged company would have annual sales of $65bn (£38bn). Time Warner's board discussed the proposal at length and sent a terse letter rejecting the offer earlier this month, saying that it was better off remaining independent.
Game of Thrones has become the most watched programme in the history of HBO after outdoing even The Sopranos in popularity.
According to Enterprise Minister Arlene Foster, the filming of the show in Northern Ireland has generated over £87m for the economy.
The filming of Season Five is expected to boost that figure by a further £20m, the minister said.
She spoke after a meeting with HBO executives Jay Loewe and Janet Graham-Borba in Los Angeles last month.