The move is not expected to be for several years because the centuries-old manor house is in a derelict condition. Reports say the couple plans to crown the manor with a domed roof.
Murdoch and Hall have a mansion in Henley, bought last year, and it is expected they will stay there while renovations on the crumbling manor take place. By taking on Great Tew Manor, they will be much closer to two of his children.
Murdoch's son James owns the rectory at Broughton and his daughter Elizabeth lives on the other side of Chipping Norton. His close colleague, former Sun and News of the World editor Rebekah Brooks is also close by near Chipping Norton with her racehorse trainer husband Charlie.
The reports in the Mail on Sunday and Daily Mail Online describe the renovation project as 'enormous' but that no expense will be spared restoring the crumbling plasterwork, damaged masonry and of course the dilapidated roof.
The future of the manor - which is a stone's throw from David and Victoria Beckham's country house and Soho Farmhouse - became big news last year when it was agreed that as part of planning permission for the controversial Mullin Automotive Museum at Enstone Airfield, a figure of £11 million would be devoted to restoration of the manor through a Section 106 agreement.
Many angry local residents wrote to West Oxfordshire District Council voicing opposition to the museum and its 28 lodges. A large number were furious that so much money was to be earmarked for renovation of the manor, owned by a wealthy estate, rather than other improvements for the community.
Perhaps with his fortune, Rupert Murdoch may offer to release that money to local causes.