The two were all smiles as they posted for pictures at the Golden Globes together on Sunday.
Rumors have been circulating for several weeks that Murdoch, 84, and Hall, 59, are a couple, though neither has publicly commented on the relationship.
In October, the media mogul and former model, who was famously involved with Mick Jagger from 1977 to 1999, got close at the Rugby World Cup final in London.
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Murdoch divorced his third wife Wendi Deng, 47, in 2013. The couple have two children together.
Hall was never officially married to Jagger, but she has four children with the Rolling Stones frontman.
The 73rd annual Golden Globes, hosted by Ricky Gervais, are being presented live from Beverly Hilton Hotel in Beverly Hills, California, on NBC.