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Murdoch, who co-chairs News Corp, and his wife Sarah are understood to have invited Jones to the annual end-of-year party at their luxurious six-bedroom home in Bellevue Hill in Sydney's east.
The 80-year-old will hold a press conference at Sydney's Hilton Hotel on Friday to reveal his next move, sources told Daily Mail Australia. The broadcaster left Sky News Australia last month.
The One Nation leader offered Jones the opportunity to join her party as soon as he revealed he was leaving Sky News Australia in lengthy Facebook post on Thursday morning.
Sky CEO Paul Whittaker and head of programs Mark Calvert told Jones they would not be renewing his program at a meeting the day after he had won the ratings in his pay TV timeslot.
Alan Jones was spotted at Matt Moran's ARIA restaurant in Circular Quay dining alongside trusted producer Jake Thrupp, 24, after his final show on Sky News on Thursday night following his shock axing.