Mr Ball is said to have impressed Mr Murdoch with his work at Fox/Liberty Networks, a joint venture with media tycoon John Malone.
Insiders believe Mr Ball, who was due for a move, is available and that his appointment will be confirmed in the next month.
A spokesman for BSkyB, which is 40 per cent owned by Murdoch's News Corp media group, said: "We are hoping to appoint someone in the next two to four weeks. The appointment will come from outside BSkyB."
The spokesman refused to comment on speculation that Mr Ball was the favourite candidate. BSkyB will be eager for a quick appointment to arrest the decline in its share price, which has fallen from 579p to 549p since Mr Booth's departure was announced on Tuesday.
BSkyB announced last week that Mr Booth, who has been with the pay-TV group since 1997, was leaving the company to run a $300m (pounds 190m) fund established by Murdoch to invest in internet ventures.
As BSkyB chief executive, he presided over the launch of its digital service but the company suffered a setback last month when its proposed takeover of Manchester United was blocked by the Monopolies and Mergers Commission.
His successor will be appointed by a committee consisting of Mr Murdoch and three other BSkyB directors, Jerome Seydoux, Sir Dennis Stevenson and Philip Bowman. However insiders believe that the appointment of Mr Ball, who is thought to be Mr Murdoch's choice, is a formality.
The importance of sports programming to BSkyB's success means that the company will be eager to appoint a chief executive with expertise in that field.
Mr Ball fits the bill, having helped to negotiate English soccer TV rights for Fox Sports International. As head of Fox/ Liberty, he presides over nine sport networks on cable, and the company has stakes in 15 others. In total, Fox/Liberty owns the rights to broadcast action from 70 US professional sports teams and its overall output reaches 62 million US homes.
Mr Ball's success recently earned him the number 66 spot in an annual list of the most important people in sport. At number one was Mr Murdoch.