Media giant Rupert Murdoch is likely to continue pursuing Time Warner Inc., the parent company of TV channels CNN and HBO, despite a recent reject of an $80 billion offer.

The deal was rejected Wednesday by Time Warner, who in a statement cited the stability of the company as a reason to continue operating on its own, according to RT.

If 21st Century Fox took over, it would sell CNN, according to The New York Times.

"The execution of Time Warner's strategic plan will continue to drive significant and sustainable value for Time Warner stockholders; the unique value of Time Warner's industry-leading businesses including its portfolio of networks and its film studio and television production business is only going to increase," according to Time Warner's statement on RT. "The board is confident that continuing to execute its strategic plan will create significantly more value for the company and its stockholders and is superior to any proposal that 21st Century Fox is in a position to offer."

Time Warner is the parent company of CNN, HBO, TNT, TBS and Warner Bros. movie studio, according to Reuters.

Murdoch currently administers the Fox channels which include National Geographic and Spanish-language news and sports channels. Fox is a percentage owner in some European media companies which are also consider mergers, according to Reuters.

The offer, which was initially reported by the New York Times on Tuesday, included 1.531 of Fox's Class A non-voting common shares and $32.42 in cash for every Time Warner share, totaling about $86.30 each.

Despite the rejection from Time Warner, sources told the Times it is unlikely Murdoch will let go, citing his history of successfully pursuing companies that have initially said no.

Supporters of the merger cite increasing competition from Internet companies Google, Amazon and Netflix which are offering increasingly popular original, on-demand shows.