Jeff Bewkes’s plan to keep Time Warner Inc. independent will probably only last so long.

The $73 billion owner of HBO, CNN and the Warner Bros. movie studio rejected a takeover bid from Rupert Murdoch’s 21st Century Fox Inc. last month, saying that its stand-alone strategy is superior to any offers Fox could make. If Chief Executive Officer Bewkes has his way, a deal won’t happen anytime soon. He isn’t interested in selling Time Warner while potential suitors including AT&T Inc. and Comcast Corp. are busy with other deals, a person with knowledge of the matter said last month.

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