Rupert Murdoch's 21st Century Fox said Wednesday that it made an offer to buy Time Warner last month.

Shares of Time Warner soared more than 15% in early trading Wednesday following the news. Time Warner owns CNN and CNNMoney.

A report first published in the New York Times revealed that Murdoch made a bid worth $85 a share in stock and cash in June.

The two companies subsequently confirmed that an offer was made and turned down by Time Warner.

Will Murdoch go away? The Times report suggests that Murdoch is unlikely to drop his plans to take over Time Warner. But a source close to Time Warner said that it is prepared to fight to stay independent and that Murdoch will have to launch a hostile bid in order to succeed.

The offer is 20% higher than where Time Warner's stock closed on Tuesday. 21st Century Fox said in a statement that it is "not currently in any discussions with Time Warner." But media industry experts in the expect that Murdoch will come back with a higher bid and that Fox may eventually succeed in its takeover effort.

"Rupert Murdoch is not going away," said Porter Bibb, managing partner at Mediatech Capital Partners. "He's going to keep upping the price until he gets it."

Time Warner said in a statement that the company is "confident that continuing to execute its strategic plan will create significantly more value" for shareholders than any proposal Fox could offer.

A deal may not pass regulatory scrutiny. Time Warner also said there is significant "regulatory risk" to trying to do a deal, meaning that antitrust regulators could block a merger.

Under terms of the bid, Fox would sell CNN to answer antitrust concerns. Sources told CNN's Cristina Alesci that ABC and ESPN owner Walt Disney Co. and CBS could be possible suitors for CNN.

But there could also be regulatory about putting the two companies' giant movie studios under the same corporate roof.

The Times also reported that Fox COO Chase Carey (and not Murdoch) reportedly met with Time Warner CEO Jeff Bewkes to discuss the deal.

One of the reasons Time Warner cited for the rejection of the offer was that the cash and stock bid involved non-voting shares of 21st Century Fox. The Murdoch family controls the voting Fox shares.

Merger makes strategic sense. If Fox is able to buy Time Warner, it would hang onto cable networks such as TBS, TNT and premium network HBO, as well as movie studio Warner Bros.

A deal would combine Time Warner's media brands with the Fox broadcast network, the 21st Century Fox movie studio, and entertainment cable networks such as FX as well as Fox News and Fox Sports 1.

It would also give the company access to a number of sports rights deals that Time Warner now holds with the NBA, the NCAA basketball tournament and Major League Baseball.

Combining the cable networks would also give the company greater leverage in negotiations with cable operators over the fees they pay to air the company's programming. There are several mergers among cable and satellite television operators which are now in the works, such as the deal between Comcast and Time Warner Cable as well as between DirectTV and AT&T.

Bibb said media companies need to get bigger as well in response to those mergers. But that could mean higher cable bills for consumers.

Rupert has been coveting Time Warner for awhile. Murdoch is said to have harbored an interest in Time Warner for some time. The possibility of an overture to Time Warner was first reported by Reuters on July 1, shortly before Murdoch, Bewkes and other media moguls met at the annual Sun Valley, Idaho media and technology conference sponsored by the investment bank Allen & Co.

Janney Montgomery Scott LLC media analyst Tony Wible identified reasons for a possible tie-up of 21st Century Fox and Time Warner in a report last month.

"However improbable it may seem, one cannot overlook this mega deal given its immense financial benefits that dovetail with a number of strategic benefits like the added sports rights, studio market share, TV production synergies, large content library, news programing synergies, distribution savings, and brand compatibility," Wible wrote at the time.

"Any deal would have to cope with overlapping networks and would very likely face more regulatory scrutiny," Wible added.

-- CNN's Cristina Alesci contributed to this report.