Oct 14 (Reuters) - Rupert Murdoch started a process that could reunite his media empire, News Corp (NWSA.O) and Fox Corp (FOXA.O) disclosed on Friday, saying they would consider combining at his behest, nearly a decade after the companies split. If a deal goes through, the combination will allow Murdoch greater control over his media assets and help the companies trim costs. Media companies are fighting decades-low growth in advertising sales and for users' attention against deep-pocketed social media and content websites. It make sense, in this context, to reunite Fox and News Corp to create a company with complementary assets and greater scale, the person familiar with the proposal said. His son Lachlan Murdoch is chairman and CEO of Fox Corp.As of market-close on Friday, News Corp had a market cap of $9.31 billion and Fox Corp was $16.84 billion, according to Refinitiv.

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