Stewart, a close ally of Tony Ball, the chief executive replaced last week by Rupert Murdoch’s son James, is expected to leave the company after February.
Insiders claim Stewart feels unable to commit himself, even though there is no animosity reported between himself and Murdoch junior.
Stewart was a leading candidate to take over from Ball. He has been at BskyB since 1996.
Stewart initially joined as head of commercial finance and became finance director in May 1998.
The appointment of 30-year-old James attracted widespread criticism.
Shareholders claimed Rupert Murdoch had exerted too much influence in getting his son to become chief executive.
Murdoch senior heads up News Corporation, which controls 34% of BSskyB.
Mark McMullen joins the private client services team from Smith & Williamson
Merger between Clear & Lane Chartered Accountants and Magma Chartered Accountants was finalised on 3 February
BDO has taken its new partner intake to 23 during the first half of its financial year, including the appointment of five partners in five weeks
The firm reports 7.6% global fee income growth for the year ending 31 December 2016