The championing of Stewart, who has been at BSkyB five years, comes as opposition is intensifying to Rupert Murdoch's plan to install his 30-year-old son James in the top job.
BSkyB shareholders are concerned that if the chairman of News Corporation gets his way, it will tighten Murdoch's grip on the British fim. News Corp has a majority stake in BSkyB of 37.5%.
BSkyB has appointed headhunters Spencer Stuart to conduct a worldwide search to fill the post, in an attempt to prevent James Murdoch from being slotted into the position.
Stewart is well respected in the City, which sees him as part of Ball's management team that has helped to make Sky such a successful company. Before joining BSkyB, Stewart worked Polygram for five years.
At not quite 40, he is the second youngest member of the board after James, who is currently chief exective of News Corp's Star TV in Asia.
The other internal candidate is BSkyB chief operating officer Richard Freudenstein. Other names linked to the job from the outside include Jim Robbins, chief executive of US cable giant Cox Communications, and the president of EchoStar, rival satellite broadcaster to News Corp's DirecTV, Michael Dugan.
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