Ball's contract expires next year, when he is expected to be replaced by the 30-year-old James Murdoch, the youngest son of the chairman, Rupert Murdoch, as part of a management shake-up.
The independent directors of BSkyB have been asked to support the appointment of James Murdoch.
Critical talks about Ball's future are underway with a decision expected before the satellite giant's annual meeting in November.
Either way, it seems increasingly unlikely that he will remain in the job after his current deal ends in June.
Shares in the giant satellite company were reported to have fallen by as much 2 per cent this week as investors responded to the speculation.
Ball joined BSkyB in 1999. Under his leadership the company has made the switch from analogue to digital transmission. Last year, the company returned to profit.
James Murdoch currently runs News Corporation's Asian satellite network Star. Previously he ran the group's US internet activities.
BSkyB refused to comment.